carla earned some money doing odd jobs last summer and put it in a savings account that earns 9% interest…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial amount), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know that $A=$300$, $r = 0.09$ (since $9%=0.09$), and $t = 1$. We need to solve for $P$.

Step2: Rearrange the formula for $P$

From $A = Pe^{rt}$, we can solve for $P$ by dividing both sides of the equation by $e^{rt}$. So $P=\frac{A}{e^{rt}}$.

Step3: Substitute the values

Substitute $A = 300$, $r=0.09$, and $t = 1$ into the formula for $P$. $P=\frac{300}{e^{0.09\times1}}=\frac{300}{e^{0.09}}$. We know that $e^{0.09}\approx1.094174$. So $P=\frac{300}{1.094174}\approx274.18$.

Answer:

$274.18$