Question

hay unit 15 - logarithmic and exponential equations: applications
question 24 of 35 (1 point) | question attempt: 1 of unlimited
use the model $a = p e^{rt}$, where $a$ is the future value of $p$ dollars invested at interest rate $r$
$2000$ grows to $2843.82$ in $8$ years under continuous compounding. find the interest rate
part 1 of 5
substitute $p = 2000$, $a = 2843.82$, $t = 8$ and solve for $r$.
part: 1 / 5
part 2 of 5
$2843.82 = 2000 e^{8r}$
isolate the exponential expression by dividing both sides by $2000$.
$\frac{\square}{\square} = e^{8r}$

Explanation:

Step1: Identify the equation

We have the continuous compounding formula \( A = Pe^{rt} \), with \( A = 2843.82 \), \( P = 2000 \), and \( t = 8 \). So the equation is \( 2843.82=2000e^{8r} \).

Step2: Isolate the exponential term

To isolate \( e^{8r} \), we divide both sides of the equation by \( 2000 \). So we calculate \( \frac{2843.82}{2000} \) to get the left - hand side.

Answer:

The numerator is \( 2843.82 \) and the denominator is \( 2000 \), so the fraction is \( \frac{2843.82}{2000} \).