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mathematics
precalculus

Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions

In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 71-x = ex
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 1.2x = (0.5) -*
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. ex+3 = πx ㅠ
In Problems 53–60, use a calculator to evaluate each expression. Round your answer to three decimal places. In 4 + In 2 log 4 + log 2
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 0.31+x = = 1.72x-1
The average annual cost of college at 4-year private colleges was $38,070 in the 2021–2022 academic year. This was a 2.1% increase from the previous year.(a) If the cost of college increases by 2.1% each year, what will be the average cost of college at a 4-year private college for the
The bones of a prehistoric man found in the desert of New Mexico contain approximately 5% of the original amount of carbon-14. If the half-life of carbon-14 is 5730 years, approximately how long ago did the man die?
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 32x + 3x - 2 = 0
Demetrius and Aniyah have just purchased a house for $650,000, with the seller holding a second mortgage of $100,000. They promise to pay the seller $100,000 plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage:(a) Simple interest at 6%
The annual growth rate of the world’s population in 2019 was k = 1.1% = 0.011. The population of the world in 2019 was 7,714,576,923. Letting t = 0 represent 2019, use the uninhibited growth model to predict the world’s population in the year 2024.
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 22x + 2x 12 = 0
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 32x+3x+1 4 = 0
In Problems 57–70, write each expression as a single logarithm. In(²7) | In (²+¹) | + In ( x + ¹) − In(x² − + - 1) X
In 2021, the federal debt was about $30 trillion. In 2021, the U.S. population was about 332 million. Assuming that the federal debt is increasing about 5.5% per year and the U.S. population is increasing about 0.7% per year, determine the per capita debt (total debt divided by population) in 2030.
In Problems 57–70, write each expression as a single logarithm. log(x² + 3x + 2) - 2 log(x + 1)
In Problems 57–70, write each expression as a single logarithm. log(x² ³)-log(² x² + 2x 31 - x² - 4 x² + 7x + 6) x + 2 T
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 16* + 4x+13=0
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 22x + 2x+2 12 = 0 -
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 57–70, write each expression as a single logarithm. - log₂ (4) + + log₂4 8 log₂√3x2 log₂
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 9x3x+1 + 1 = 0
In Problems 57–70, write each expression as a single logarithm. 21 log, √x + log3 (9x²) - log39
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 25x8.5x = -16
The formulacan be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year.(a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6%?(b) How many years will it take to
In Problems 57–70, write each expression as a single logarithm. 2 loga (5x³) - log₁ (2x + 3) 2
Problems 63–66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.A zero-coupon bond can be redeemed in 20 years for $10,000. How much should you be willing to pay for it now
Problems 63–66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.If Hakim pays $15,334.65 for a $25,000 face-value, zero-coupon bond that matures in 8 years, what is his
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 36*6.6* = -9
Open the “Exponential Functions” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) I n the interactive figure, the graph of f (x) = c · ax−h + k is drawn. Use the sliders to set the value of c to 1, a
The population of a midwestern city is declining according to the exponential law.(a) If N is the population of the city and t is the time in years, express N as a function of t.(b) If the population decreased from 900,000 to 800,000 from 2020 to 2022, what will the population be in 2024?
Ifthen M = _______. log, M 8 log, 7 log, 8 then M
In Problems 5 – 44, solve each logarithmic equation. Express irrational solutions in exact form. log₂ (5x) = 4
In Problems 4 – 6, find f º g, g º f, f º f, and g º g for each pair of functions. State the domain of each composite function. f(x) = = x+1 x-1 g(x) = 1 X
A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 7 weeks and obtains the following data:(a) Using a graphing utility, draw a scatter plot with week as the independent variable.(b) Using a graphing utility, build an exponential
Approximate the solution(s) to x3 − 2x + 2 = 0 using a graphing utility.
Open the “Logarithmic Functions” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Set the values of a to 2, c to 1, h to 0, and k to 0. Use the slider to adjust the value of h from −3 to 3. Pay
In Problems 57–70, write each expression as a single logarithm. 2 log₂ (x + 1) = log₂ (x + 3) - log₂ (x - 1)
Problems 69–72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the
In Problems 67–74, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) y = log3 x (E) y = log 3x - 1 (B) y (F) y = log3 (-x) log2 (x - 1) (C) y = -log3 x (G) y = log3(1-x) (D) y = -log3 (-x) (H) y = 1 log 3 x
In Problems 57–70, write each expression as a single logarithm. 3 logs (3x + 1) - 2 logs (2x - 1) - log, x
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 2.49x + 11 7* + 5 = 0
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 4* - 10.4-* = 3
Problems 69–72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. 3x - 14.3-* = 5
Problems 69–72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. ex + e-x 2 = 1
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. ex + e-* 2 = 3
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. ex - e-x 2 || 2
Explain in your own words what the term compound interest means. What does continuous compounding mean?
In Problems 45–76, solve each exponential equation. Express irrational solutions in exact form. ex 2 e-x || -2
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log √5 8
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the remainder R when f (x) = 6x3 + 3x2 + 2x − 11 is divided by g(x) = x − 1. Is g a factor
In Problems 75–90, use the given function f.(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f −1, the inverse of f.(e) Find the domain and the range of f −1.(f) Graph f −1.f (x) = ln(x − 3)
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. The function f(x) = X x - 2 is one-to-one. Find f-¹.
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log5 (x+1) log4(x - 2) = 1 -
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. loge
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log₂ (x1) logo (x + 2) = 2
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the real zeros of f (x) = x5 − x4 − 15x3 − 21x2 − 16x − 20
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Solve: log₂ (x + 3) = 2 log₂ (x - 3)
In Problems 75–90, use the given function f.(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f −1, the inverse of f.(e) Find the domain and the range of f −1.(f) Graph f −1.f (x) = −ln(−x)
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula. y = log 4 x
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e2x = = x + 2
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. ex = x x2
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Factor completely: 2x4 + 6x3 − 50x2 − 150x
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If f (x) = 5x2 + 4x − 8 and g (x) = 3x − 1, find (f º g)(x).
In Problems 75–90, use the given function f.(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f −1, the inverse of f.(e) Find the domain and the range of f −1.(f) Graph f −1. f(x) = 1/1 -logx - 5
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. 2x² - 5x - 4 x - 7 find all vertical asymptotes, horizontal asymptotes, and oblique asymptotes, if
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. In x = x³ - 1
In Problems 75–90, use the given function f.(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f −1, the inverse of f.(e) Find the domain and the range of f −1.(f) Graph f −1. f(x) = = -log(2x)
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. In x = -x²
If f (x) = log x, g(x) = 2x, 2 and h(x) = 4x, find: (a) (fog)(x). (b) (gof)(x). (c) (fog)(3) (d) (foh)(x). (e) (f oh)(8) What is the domain of f o g? What is the domain of g o f? What is the domain of f o h?
If f (x) = ln x, g(x) = ex, and h(x) = x2, find: (a) (fog)(x). (b) (gof)(x). (c) (fog)(5) (d) (f o h)(x). What is the domain of f o h? (e) (foh)(e) What is the domain of f o g? What is the domain of g o f?
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. ex + ln x = 4
f (x) = log3 (x + 5) and g(x) = log3 (x − 1). (a) Solve f(x) = 2. What point is on the graph of f? (b) Solve g(x) = 3. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g)(x) = 3. (e) Solve (f g)(x) = 2.
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the domain and range of f (x) = −2x2 − 8x + 1.
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. ex In x = 4
In Problems 77–90, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e-x = In x
f (x) = log2 (x + 3) and g(x) = log2 (3x + 1). (a) Solve f(x) = 3. What point is on the graph of f? (b) Solve g(x) = 4. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g)(x) = 7. (e) Solve (f g)(x) = 2.
Problems 76 – 85. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If f (x) = x2 − 4x − 3, find an equation of the secant line containing the points (3, f (3)) and
Problems 76 – 85 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the difference quotient for f (x) = 3x − 5.
In Problems 91–114, solve each equation. log, (3) = 3
Find the value of log₂3.log34 log45 log, 6 log67.log78.
In Problems 87–96, express y as a function of x. The constant C is a positive number.ln y = 2 ln x − ln( x + 1) + ln C
Find the value of log₂2 log₂4 log₂8 log₂2".
In Problems 91–114, solve each equation.log3 x = 2
Find the value of log₂4 log46 log68.
Find the value of log₂ 3 log 34 log, (n + 1) .logn+12. .
In Problems 91–114, solve each equation.log5 x = 3
Show that loga (√x + √x − 1) + loga (√x - √x − 1) = 0.
In Problems 91–114, solve each equation.log2 (3x + 4) = 5
In Problems 91–114, solve each equation.log x 16 = 2
Show that loga (x + √x² − 1) + loga(x − √x² − 1) = 0. - -
If f(x) = loga x, show that f(x+h)-f(x) h = 1/h ² ( 1 + 4) ¹/², log 1 + h = 0.
In Problems 91–114, solve each equation.ln ex = 5
Show that ln(1 + e²x) = 2x + ln(1 + e−²x).
The value V of a Honda Civic LX that is t years old can be modeled by V(t) = 19, 705(0.848)t.(a) According to the model, when will the car be worth $14,000?(b) According to the model, when will the car be worth $10,000?(c) According to the model, when will the car be worth $7500? CIVIC wa
In Problems 106–111, solve each equation. Express irrational solutions in exact form. log₂ (x + 1) - log4 x = 1

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