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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, refer to Table 8.Graph the exponential equation on the scatter diagram. 12 x f(x) 555 383 3 4 6 307 210 158 12 Table 8
Condense the expression 5ln(b) + ln(c) + ln(4−a)/2 to a single logarithm.
For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.The half-life of Radium-226 is 1590 years. What is the annual decay rate? Express the decimal result to four significant digits and the percentage to two
The population of a lake of fish is modeled by the logistic equation P(t) = 16, 120/1 + 25e−0.75t, where t is time in years. To the nearest hundredth, how many years will it take the lake to reach 80% of its carrying capacity? For the following exercises, use a graphing utility to create a
For the following exercises, refer to Table 8.Use the intersect feature to find the value of x for which f(x) = 250. f(x) 1 555 2 383 3 307 Table 8 4 210 5 158 6 122
Condense the expression 3log7v + 6log7w − log7u/3 to a single logarithm.
For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.The half-life of Erbium-165 is 10.4 hours. What is the hourly decay rate? Express the decimal result to four significant digits and the percentage to two
For the following exercises, start with the graph of f(x) = 4x. Then write a function that results from the given transformation.Shift f(x) 5 units right
For the following exercises, solve for x by converting the logarithmic equation to exponential form.ln(x) = 2
For the following exercises, refer to Table 9.Use a graphing calculator to create a scatter diagram of the data. x 1 f(x) 5.1 2 6.3 3 7.3 Table 9 4 7.7 5 8.1 6 8.6
What is carbon dating? Why does it work? Give an example in which carbon dating would be useful.
Find an exponential equation that passes through the points (0, 4) and (2, 9).
What is a carrying capacity? What kind of model has a carrying capacity built into its formula? Why does this make sense?
Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points. X f(x) 1 3 2 0.9 Table 1 3 0.27 4 0.081
Find an exponential equation that passes through the points (2, 2.25) and (5, 60.75).
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Rewrite log8.5(614.125) = a as an equivalent exponential equation.
Suppose an investment account is opened with an initial deposit of $10,500 earning 6.25% interest, compounded continuously. How much will the account be worth after 25 years?
Graph the function f(x) = 4 (1/8)x and its reflection about the y-axis on the same axes, and give the y-intercept. 6-5-4-3-2 54 Figure 1 x
Solve for x by converting the logarithmic equation log1/7 (x) = 2 to exponential form.
Determine whether the data from the table could best be represented as a function that is linear, exponential, or logarithmic. Then write a formula for a model that represents the data.
With what kind of exponential model would half-life be associated? What role does half-life play in these models?
The population of a pod of bottlenose dolphins is modeled by the function A(t) = 8(1.17)t, where t is given in years. To the nearest whole number, what will the pod population be after 3 years?
Determine whether the function y = 156(0.825)t represents exponential growth, exponential decay, or neither. Explain.
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
The population of a herd of deer is represented by the function A(t) = 205(1.13)t, where t is given in years. To the nearest whole number, what will the herd population be after 6 years?
With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?
The graph below shows transformations of the graph of f(x) = (1/2)x. What is the equation for the transformation? y -4-3-2-1 0 IT 2 3 4 5 6 7 8 X
Drew wants to save $2,500 to go to the next World Cup. To the nearest dollar, how much will he need to invest in an account now with 6.25% APR, compounding daily, in order to reach his goal in 4 years?
What is regression analysis? Describe the process of performing regression analysis on a graphing utility.
Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.
For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph.y = 10.209e−0.294x 16 14 12 10 8+ 6 4 2 . 1 2 3 4 5 6 7 8 9 10 (a) Figure 7
For the following exercises, use the logistic growth model f(x) Find and interpret f(0). Round to the nearest tenth. 150 1+ 8e-2x1
What might a scatterplot of data points look like if it were best described by a logarithmic model?
What is an order of magnitude? Why are orders of magnitude useful? Give an example to explain.
Graph the function f(x) = 5(0.5)−x and its reflection across the y-axis on the same axes, and give the y-intercept.
A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years?
What does the y-intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
For the following exercises, use the logistic growth model f(x) Find the carrying capacity. 150 1+ 8e-2x1
For the following exercises, use the logistic growth model f(x) Find and interpret f(4). Round to the nearest tenth. 150 1+ 8e-2x1
The temperature of an object in degrees Fahrenheit after t minutes is represented by the equation T(t) = 68e−0.0174t + 72. To the nearest degree, what is the temperature of the object after one and a half hours?
For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph.y = 4.607 + 2.733ln(x) 16 14 12 10 8 6 4 2 1 2 3 4 5 6 7 (a) Figure 7 + X 8 9 10 16 14 12 10 8 6 NA 4 2 y 1 2 3 4
For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph.y = 2.104(1.479)x 16 14 12 10 8 6 4 2 y 1 2 3 . 4 5 6 7 (a) Figure 7 8 00 x++ 9
Hsu-Mei wants to save $5,000 for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with 7.5% APR, compounded daily, in order to reach her goal in 3 years?
Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept. Coco Figure 1 x
For the following exercises, match the given function of best fit with the appropriate scatterplot in Figure 7 through Figure 11. Answer using the letter beneath the matching graph.y = 14.005/1+2.79e−0.81 16+ 14 12 10 8 6+ 4 1 2 3 4 5 6 7 (a) Figure 7 8 00 +X 9
Rewrite e1/2 = m as an equivalent logarithmic equation.
For the following exercises, use the logistic growth model f(x) Graph the model. 150 1+ 8e-2x1
The graph of f(x) = 6.5x is reflected about the y-axis and stretched vertically by a factor of 7. What is the equation of the new function, g (x)? State its y-intercept, domain, and range. 6-5-4- Figure 1 56 x
The graph here shows transformations of the graph of f(x) = 2x. What is the equation for the transformation? 6-5-4 48 中 Figure 1 [L AD x
For the following exercises, use the logistic growth model f(x) Rewrite f(x) = 1.68(0.65)x as an exponential equation with base e to five significant digits. 150 1+ 8e-2x1
Evaluate log(10,000,000) without using a calculator.
To the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t) = 175/1 + 6.995e−0.68t ? What is the carrying capacity?
For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.
Graph the function g (x) = log(12 − 6x) + 3.
Rewrite the exponential model A(t) = 1550(1.085)x as an equivalent model with base e. Express the exponent to four significant digits.
State the domain, vertical asymptote, and end behavior of the function f(x) = log5 (39 − 13x) + 7.
For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.
What is the y-intercept on the graph of the logistic model given in the previous exercise?
A logarithmic model is given by the equation h(p) = 67.682 − 5.792ln(p). To the nearest hundredth, for what value of p does h(p) = 62?
Rewrite log17(4913) = x as an equivalent exponential equation.
A logistic model is given by the equationTo the nearest hundredth, for what value of t does P(t) = 45? P(t) = 90 1 +5e-0.42t
For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. 4 f(x) 9.429 x 5 6 7 9.972 10.415 10.79 8 9 10 11 12 13
Rewrite ln(s) = t as an equivalent exponential equation.
Rewrite logt (96) − logt (8) in compact form.
For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. x f(x) 1.25 2.25 5.75 8.75 3.56 4.2 5.65 6.75 7.25 12.68
Rewrite a − 2/5 = b as an equivalent logarithmic equation.
For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t) Graph the function. || 1000 1+9e-0. -0.6t
For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t) What is the initial population of fish? || 1000 1+9e-0. -0.6t
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x .Graph the population model to show the population over a span of 3 years.
Rewrite e−3.5 = h as an equivalent logarithmic equation.
Use properties of logarithm to expand ln (y3 z2 · 3√ x − 4).
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.What was the initial population of koi?
Solve for xlog64(x) = (1/3) to exponential form.
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.How many koi will the pond have after one and a half years?
For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t) To the nearest tenth, what is the doubling time for the fish population? || 1000 1+9e-0. -0.6t
Evaluate log5 (1/125) without using a calculator.
Rewrite 163x − 5 = 1000 as a logarithm. Then apply the change of base formula to solve for x using the natural log. Round to the nearest thousandth.
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.How many months will it take before there are 20 koi in the pond?
Evaluate log(0.000001) without using a calculator.
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.
For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t) To the nearest tenth, how long will it take for the population to reach 900? || 1000 1+9e-0. -0.6t
Evaluate log(4.005) using a calculator. Round to the nearest thousandth.
For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x) = 558/1 + 54.8e−0.462x, where x is given in years.Graph the population model to show the population over a span of 10 years.
For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P(t) What is the carrying capacity for the fish population? Justify your answer using the graph of P. || 1000 1+ 9e-0.6t
Evaluate ln(e−0.8648) without using a calculator.
Find the exact solution for 10e4x + 2 + 5 = 56. If there is no solution, write no solution.
For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x) = 558/1 + 54.8e−0.462x , where x is given in years.What was the initial population of wolves transported to the habitat?
Evaluate ln (3√18) using a calculator. Round to the nearest thousandth.
Find the exact solution for −5e−4x − 1 − 4 = 64. If there is no solution, write no solution.
For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x) = 558/1 + 54.8e−0.462x , where x is given in years.How many wolves will the habitat have after 3 years?
Recall the formula for calculating the magnitude of an earthquake,Show each step for solving this equation algebraically for the seismic moment S. M = 3 log S S 0
Graph the function g(x) = log(7x + 21) − 4.
Find the exact solution for 2x − 3 = 62x − 1 . If there is no solution, write no solution.
For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x) = 558/1 + 54.8e−0.462x , where x is given in years.How many years will it take before there are 100 wolves in the habitat?
Graph the function h(x) = 2ln(9 − 3x) + 1.
Find the exact solution for e2x − ex − 72 = 0. If there is no solution, write no solution.
For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P(x) = 558/1 + 54.8e−0.462x , where x is given in years.Use the intersect feature to approximate the number of years it will take before the population of the
State the domain, vertical asymptote, and end behavior of the function g (x) = ln(4x + 20) − 17.
What is the y-intercept of the logistic growth model y = c/1+ae−rx ? Show the steps for calculation. What does this point tell us about the population?
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