florence opened a savings account and deposited $1,967.00. the account earns 3% 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 deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal form

The annual interest rate $r = 3%=0.03$, the principal amount $P = 1967$, and the number of years $t = 2$.

Step3: Substitute the values into the formula

$A=1967\times e^{0.03\times2}$. First, calculate the exponent: $0.03\times2 = 0.06$. Then, find the value of $e^{0.06}$. Using a calculator, $e^{0.06}\approx1.061836547$. Multiply by the principal: $A = 1967\times1.061836547$. $A\approx1967\times1.061836547 = 2088.632488$.

Step4: Round to the nearest cent

Rounding $2088.632488$ to the nearest cent gives $A\approx2088.63$.

Answer:

$2088.63$