Question

every year, the cost of solar panels drops by roughly 6%. if solar panels currently cost $5,918 per kilowatt, what will the per - kilowatt cost be in 8 years? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time in years.
Here, $P = 5918$, $r = 0.06$ (since 6% = 0.06), and $t = 8$.

Step2: Substitute the values into the formula

Substitute $P = 5918$, $r = 0.06$, and $t = 8$ into the formula:
$A = 5918(1 - 0.06)^8$
First, calculate $(1 - 0.06) = 0.94$.
Then, calculate $0.94^8$. We know that $0.94^8\approx0.60956893$.
Now, multiply this by 5918: $A = 5918\times0.60956893$.

Step3: Calculate the final amount

$5918\times0.60956893\approx5918\times0.609569\approx3607.43$ (rounded to the nearest cent)

Answer:

$\$3607.43$