malik puts $2,000.00 into an account to use for school expenses. the account earns 5% 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

The interest rate $r = 5%=0.05$, the principal $P = 2000$, and the time $t = 10$.

Step3: Substitute the values into the formula

Substitute $P = 2000$, $r = 0.05$, and $t = 10$ into the formula $A = Pe^{rt}$. We get $A=2000\times e^{0.05\times10}$.

Step4: Calculate the exponent

First, calculate $0.05\times10 = 0.5$. Then, find the value of $e^{0.5}$. Using a calculator, $e^{0.5}\approx1.648721$.

Step5: Calculate the final amount

Multiply $2000$ by $e^{0.5}$. So, $A = 2000\times1.648721=3297.442$.

Step6: Round the answer

Rounding to the nearest cent, $A\approx3297.44$.

Answer:

$3297.44$