dalton owns a small manufacturing business. in 1 year, he wants to buy a machine that costs $8,000.00. 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 know that $A=$8000$, $r = 0.15$, and $t = 1$. 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

Substitute $A = 8000$, $r=0.15$, and $t = 1$ into the formula $P=\frac{A}{e^{rt}}$. We get $P=\frac{8000}{e^{0.15\times1}}=\frac{8000}{e^{0.15}}$.

Step4: Calculate the value of $P$

We know that $e^{0.15}\approx1.161834$. Then $P=\frac{8000}{1.161834}\approx6885.83$.

Answer:

$6885.83$