dirk earned some money doing odd jobs last summer and put it in a savings account that earns 6% 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 investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We are given that $A=$1000$, $r = 0.06$ (since $6%=0.06$), and $t = 10$.

Step2: Solve for $P$

Starting with $A = Pe^{rt}$, we can isolate $P$ by dividing both sides of the equation by $e^{rt}$. So $P=\frac{A}{e^{rt}}$. Substitute the given values: $P=\frac{1000}{e^{0.06\times10}}$. First, calculate the exponent: $0.06\times10 = 0.6$. Then, find $e^{0.6}\approx1.822119$. So $P=\frac{1000}{1.822119}\approx548.81$.

Answer:

$548.81$