lafarge deposited $100 at 9 percent interest compounded continuously. how much money did she have at the end…

Explanation:

Step1: Identify the formula

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

Step2: Convert the interest rate to decimal

The annual interest rate $r = 9%=0.09$, the principal amount $P = 100$, and the number of years $t = 9$.

Step3: Substitute values into the formula

Substitute $P = 100$, $r = 0.09$, and $t = 9$ into the formula $A = Pe^{rt}$. So $A=100\times e^{0.09\times9}$.

Step4: Calculate the exponent

First, calculate $0.09\times9 = 0.81$. Then we have $A = 100\times e^{0.81}$.

Step5: Find the value of $e^{0.81}$

Using a calculator, $e^{0.81}\approx2.2479$.

Step6: Calculate the final amount

Multiply 100 by $2.2479$, so $A = 100\times2.2479 = 224.79$.

Answer:

$224.79$