seth puts $800.00 into an account to use for school expenses. the account earns 15% interest, compounded…

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal form

Given $r = 15%=0.15$, $P=$800$, and $t = 5$ years.

Step3: Substitute the values into the formula

$A=800\times e^{0.15\times5}$.

Step4: Calculate the exponent

First, calculate $0.15\times5 = 0.75$. Then, find $e^{0.75}$. Using a calculator, $e^{0.75}\approx2.117$.

Step5: Calculate the final amount

$A = 800\times2.117=1693.67$.

Answer:

$1693.67$