wyatt is saving up money to buy a car. wyatt puts $5,871.00 into an account which earns 10% interest…

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 $r = 10%=0.1$. The principal amount $P = 5871$, and the time $t = 1$ year.

Step3: Substitute the values into the formula

Substitute $P = 5871$, $r=0.1$, and $t = 1$ into the formula $A = Pe^{rt}$. We get $A=5871\times e^{0.1\times1}$.

Step4: Calculate the value of $A$

First, calculate $e^{0.1}$. Using a calculator, $e^{0.1}\approx1.105170918$. Then, $A = 5871\times1.105170918\approx6493.01$.

Answer:

$6493.01$