지수함수와 로그함수 전체 문제

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

$f(x)={e}^{x},$ for $f(3)$

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

$f(x)=-2{e}^{x-1},$ for $f(-1)$

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

$f(x)=2.7{(4)}^{-x+1}+1.5,$ for $f(-2)$

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

$f(x)=1.2{e}^{2x}-0.3,$ for $f(3)$

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

$f(x)=-\frac{3}{2}{(3)}^{-x}+\frac{3}{2},$ for $f(2)$

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

$(0,3)$ and $(3,375)$

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

$(3,222.62)$ and $(10,77.456)$

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

$(20,29.495)$ and $(150,730.89)$

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

$(5,2.909)$ and $(13,0.005)$

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

$(11,310.035)$ and $(25,356365.2)$

Repeat the previous exercise to find the formula for the APY of an account that compounds daily. Use the results from this and the previous exercise to develop a function $I(n)$ for the APY of any account that compounds $n$ times per year.

Recall that an exponential function is any equation written in the form $f(x)=a\cdot {b}^{x}$ such that $a$ and $b$ are positive numbers and $b\ne 1.$ Any positive number $b$ can be written as $b={e}^{n}$ for some value of $n$ . Use this fact to rewrite the formula for an exponential function that uses the number $e$ as a base.

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?

A car was valued at $38,000 in the year 2007. By 2013, the value had depreciated to $11,000 If the car’s value continues to drop by the same percentage, what will it be worth by 2017?

Jaylen wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?

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 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: solve the compound interest formula for the interest rate.)

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 make if interest compounded continuously?

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, quarterly, monthly, and continuously.

For the following exercises, describe the end behavior of the graphs of the functions.

$f(x)=-5{(4)}^{x}-1$

For the following exercises, describe the end behavior of the graphs of the functions.

$f(x)=3{\left(\frac{1}{2}\right)}^{x}-2$