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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

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?
Use the definition of a logarithm to find the exact solution for 4log(2n) − 7 = −11.
For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal
For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.e5x = 17
For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.3(1.04)3t
For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.34x−5 =
For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal
For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth.7e3x − 5 + 7.9 = 47
For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth.ln(3) + ln(4.4x + 6.8) = 2
For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth.log(−0.7x − 9) = 1 + 5log(5)
For the following exercises, use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth.Atmospheric pressure P in pounds per square inch is
Unless indicated otherwise, round all answers to the nearest ten-thousandth.The magnitude M of an earthquake is represented by the equation where E is the amount of energy released by the
Use the definition of a logarithm along with the one to-one property of logarithms to prove that blogbx = x.
Recall the formula for continually compounding interest, y = Aekt. Use the definition of a logarithm along with properties of logarithms to solve the formula for time t such that t is equal to a
Recall the compound interest formula A = a (1 + r/k)kt. Use the definition of a logarithm along with properties of logarithms to solve the formula for time t.
For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best
Kyoko has $10,000 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $15,000 by the time she finishes graduate school in 6
For the following exercises, solve for the indicated value, and graph the situation showing the solution point.The formula for measuring sound intensity in decibels D is defined by the equation D =
Alyssa opened a retirement account with 7.25% APR in the year 2000. Her initial deposit was $13,500. How much will the account be worth in 2025 if interest compounds monthly? How much more would she
For the following exercises, solve for the indicated value, and graph the situation showing the solution point.The population of a small town is modeled by the equation P = 1650e0.5t where t is
For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best
For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best
An investment account with an annual interest rate of 7% was opened with an initial deposit of $4,000. Compare the values of the account after 9 years when the interest is compounded annually,
Newton’s Law of Cooling states that the temperature T of an object at any time t can be described by the equation T = Ts + (T0 − Ts )e−kt, where Ts is the temperature of the surrounding
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 would likely represent a
Is the following true: log3 (27)/log4 (1/64) = −1? Verify the result.
For the following exercises, solve the equation for x, if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution.log9
For the following exercises, rewrite each equation in logarithmic form.ek = h
For the following exercises, use the definition of a logarithm to solve the equation.10 − 4ln(9 − 8x) = 6
For the following exercises, sketch the graphs of each pair of functions on the same axis. f(x) = log(x) and g(x) = log (x) 2
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.log6 (5.38)
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log18 (x) = 2
For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log3 (x) = 2
For the following exercises, suppose log5 (6) = a and log5 (11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps
For the following exercises, match each function in Figure 17 with the letter corresponding to its graph.f(x) = ln(x) y 2- 14 0 -1+ 2 Figure 17 3 A B C D E
For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the
For the following exercises, use logarithms to solve.e2x − ex − 6 = 0
For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range.h(x) = 2x + 3
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log2 (x) = −3
For the following exercises, suppose log5 (6) = a and log5 (11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps
For the following exercises, match each function in Figure 17 with the letter corresponding to its graph.g(x) = log2 (x) y 2+ 1+ 0 -1+ 2 Figure 17 3 A B D E x
For the following exercises, use the compound interest formula, After a certain number of years, the value of an investment account is represented by the equation What is the value of the
For the following exercises, use logarithms to solve.3e3 − 3x + 6 = −31
For the following exercises, match each function in Figure 17 with the letter corresponding to its graph.h(x) = log5 (x) 2+ 14 0 -14 2 Figure 17 3 B -C D E X
For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range.f(x) = 2x − 2
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log5 (x) = 2
For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. log (100) = -2
For the following exercises, suppose log5 (6) = a and log5 (11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps
For the following exercises, use the compound interest formula, What was the initial deposit made to the account in the previous exercise? A(t) = P(1 + 7)". r nt
For the following exercises, match each function in Figure 17 with the letter corresponding to its graph.j(x) = log25(x) 2 1+ 0 -14 2 Figure 17 3 A B C D E X
For the following exercises, describe the end behavior of the graphs of the functions.f(x) = −5(4)x − 1
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log3 (x) = 3
For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. 1 log324 (18) = 2
For the following exercises, use properties of logarithms to evaluate without using a calculator.log3 (1/9) − 3log3 (3)
For the following exercises, describe the end behavior of the graphs of the functions. f(x) = 3 ( ¹ ) * - 2 - 2
For the following exercises, use properties of logarithms to evaluate without using a calculator. 6log(2) + log, (64) 3logg (4)
For the following exercises, use the compound interest formula, How many years had the account from the previous exercise been accumulating interest? A(t) = P(1 + 7)". r nt
For the following exercises, match each function in Figure 18 with the letter corresponding to its graph. f(x) = log1/3 (x) -5-4-3-2-1 Figure 18 -X
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log2 (x) = 6
For the following exercises, use properties of logarithms to evaluate without using a calculator. 2log,(3) — 4log,(3) + log, (729) -
For the following exercises, use the definition of a logarithm to solve the equation.5log7 (n) = 10
For the following exercises, use the compound interest formula, An account is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi-annually. What will the account be worth
For the following exercises, describe the end behavior of the graphs of the functions.f(x) = 3(4)−x + 2
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log9 (x) = 1/2
For the following exercises, match each function in Figure 18 with the letter corresponding to its graph.g(x) = log2 (x) Figure 18 3 4 5 -x
For the following exercises, use the definition of a logarithm to solve the equation.−8log9 (x) = 16
For the following exercises, use the compound interest formula, How much more would the account in the previous exercise have been worth if the interest were compounding weekly? A(t) = P(1 + 7)". r nt
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) 4 units upward
For the following exercises, match each function in Figure 18 with the letter corresponding to its graph.h(x) = log 3/4 (x) 5+ Figure 18 34
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.log3 (22)
For the following exercises, use the definition of a logarithm to solve the equation.4 + log2 (9k) = 2
For the following exercises, use the compound interest formula, Solve the compound interest formula for the principal, P. A(t) = P(1 + 7)". r nt
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) 3 units downward
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log6 (x) = −3
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.log8 (65)
For the following exercises, sketch the graphs of each pair of functions on the same axis.f(x) = log(x) and g(x) = 10x
For the following exercises, use the definition of a logarithm to solve the equation.2log(8n + 4) + 6 = 10
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) 2 units left
For the following exercises, use the graphs to write an equation for the function. IIIT 2000 -10-8-- y انا - انا el m S5 DII 6 8 10 x
For the following exercises, solve for x by converting the logarithmic equation to exponential form.log(x) = 3
For the following exercises, determine the function described and then use it to answer the question.The period T, in seconds, of a simple pendulum as a function of its length l, in feet, is given by
For the following exercises, use the graphs to write an equation for the function. -10-8-6-4- II y PI HE 4 6 8 10 IITO X
For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rational zeros. All real solutions are rational.f(x) = 4x3 − 4x2 − 13x − 5
For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rational zeros. All real solutions are rational.f(x) = 8x3 − 6x2 − 23x + 6
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.Contains (1, −6) has the shape of f(x) = 3x2 .
The Oxford Dictionary defines the word nominal as a value that is “stated or expressed but not necessarily corresponding exactly to the real value.” Develop a reasonable argument for why the term
For the following exercises, state the domain and range of the function.f(x) = log2 (12 − 3x) − 3
For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. In y 1-y
For the following exercises, condense to a single logarithm if possible.ln(a) − ln(d) − ln(c)
For the following exercises, state the domain, vertical asymptote, and end behavior of the function.h(x) = −log(3x − 4) + 3
For the following exercises, use logarithms to solve.−5e9x − 8 − 8 = −62
For the following exercises, rewrite each equation in logarithmic form.m−7 = n
For the following exercises, condense each expression to a single logarithm using the properties of logarithms.ln(6x9) − ln(3x2)
For the following exercises, state the domain, range, and x- and y-intercepts, if they exist. If they do not exist, write DNE.h(x) = log4 (x − 1) + 1
For the following exercises, use logarithms to solve.e2x − ex − 132 = 0
For the following exercises, rewrite each equation in logarithmic form.n4 = 103
For the following exercises, find the formula for an exponential function that passes through the two points given.(−2, 6) and (3, 1)
For the following exercises, condense each expression to a single logarithm using the properties of logarithms.2log(x) + 3log(x + 1)
For the following exercises, state the domain, range, and x- and y-intercepts, if they exist. If they do not exist, write DNE.f(x) = log(5x + 10) + 3

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