jasmine owns a small manufacturing business. in 1 year, she wants to buy a machine that costs $7,000.00. if…

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, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We need to solve for $P$. Rearranging the formula gives $P=\frac{A}{e^{rt}}$.

Step2: Identify the values of $A$, $r$, and $t$

We know that $A = 7000$ (the amount of money needed in 1 year), $r=0.07$ (since 7% = 0.07), and $t = 1$ (1 year).

Step3: Substitute the values into the formula

$P=\frac{7000}{e^{0.07\times1}}=\frac{7000}{e^{0.07}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.07}\approx1.072508$. Then $P=\frac{7000}{1.072508}\approx6526.78$.

Answer:

$6526.78$