지수함수와 로그함수 전체 문제

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

What was the initial deposit made to the account in the previous exercise?

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

How many years had the account from the previous exercise been accumulating interest?

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

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 in $20$ years?

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

How much more would the account in the previous exercise have been worth if the interest were compounding weekly?

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

Solve the compound interest formula for the principal, $P$ .

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

Use the formula found in the previous exercise to calculate the initial deposit of an account that is worth $\text{\textdollar}14,472.74$ after earning $5.5\%$ interest compounded monthly for $5$ years. (Round to the nearest dollar.)

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

How much more would the account in the previous two exercises be worth if it were earning interest for $5$ more years?

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

Use properties of rational exponents to solve the compound interest formula for the interest rate, $r.$

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $9,000 and was worth $13,373.53 after 10 years.

For the following exercises, use the compound interest formula, $A(t)=P{\left(1+\frac{r}{n}\right)}^{nt}.$

Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded monthly, had an initial deposit of $5,500, and was worth $38,455 after 30 years.

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

$y=3742{(e)}^{0.75t}$

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

$y=150{(e)}^{\frac{3.25}{t}}$

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

$y=2.25{(e)}^{-2t}$

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

Suppose an investment account is opened with an initial deposit of $\text{\textdollar}12,000$ earning $7.2\%$ interest compounded continuously. How much will the account be worth after $30$ years?

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.

How much less would the account from Exercise 42 be worth after $30$ years if it were compounded monthly instead?

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

$f(x)=2{(5)}^{x},$ for $f(-3)$

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

$f(x)=-{4}^{2x+3},$ for $f(-1)$

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 $f(-2)$