Question

after it has been harvested, corn stored at a particular temperature will lose market value at a rate of 7% per day. if a corn harvest worth $92,389 is being stored at that temperature, what will its market value be in 5 days? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (or initial value), $r$ is the rate of decay (as a decimal), and $t$ is the time in days.
Here, $P = 92389$, $r = 0.07$ (since 7% = 0.07), and $t = 5$.

Step2: Substitute the values into the formula

Substitute the given values into the formula: $V = 92389(1 - 0.07)^5$.
First, calculate $(1 - 0.07) = 0.93$.
Then, calculate $0.93^5$. Let's compute that: $0.93^5 \approx 0.93\times0.93\times0.93\times0.93\times0.93 \approx 0.695688$.

Step3: Calculate the final value

Now, multiply this by the initial value: $V = 92389\times0.695688$.
Calculate that: $92389\times0.695688 \approx 92389\times0.695688 \approx 64274.42$.

Answer:

$\$64274.42$