1. number: 25 points\nhenry opened a savings account and deposited $400.00 as principal. the account earns…

Explanation:

Step1: Identify the formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The interest rate $r = 2%=0.02$. The principal $P = 400$ and the time $t = 8$ years.

Step3: Substitute values into the formula

Substitute $P = 400$, $r = 0.02$, and $t = 8$ into the formula $A = Pe^{rt}$. So $A=400\times e^{0.02\times8}$.

Step4: Calculate the exponent

First, calculate $0.02\times8 = 0.16$. Then, find the value of $e^{0.16}$. Using a calculator, $e^{0.16}\approx1.17351$.

Step5: Calculate the final amount

Multiply $400$ by $1.17351$. So $A = 400\times1.17351 = 469.404\approx469.40$.

Answer:

$469.40$