robert earned some money doing odd jobs last summer and put it in a savings account that earns 1% 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=$700$, $r = 0.01$ (since $1%=0.01$), and $t = 10$. We need to solve for $P$.

Step2: Rearrange the formula to solve for $P$

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

Step3: Substitute the given values into the formula for $P$

Substitute $A = 700$, $r=0.01$, and $t = 10$ into the formula $P=\frac{A}{e^{rt}}$. We get $P=\frac{700}{e^{0.01\times10}}=\frac{700}{e^{0.1}}$. Since $e^{0.1}\approx1.10517$, then $P=\frac{700}{1.10517}\approx633.39$.

Answer:

$633.39$