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 $58,280 is being stored at that temperature, what will its market value be in 6 days? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for depreciation

The market value decreases by a percentage each day, so we use the formula for exponential decay: $V = P(1 - r)^t$, where $P$ is the initial value, $r$ is the daily rate of decrease, and $t$ is the time in days.
Here, $P = 58280$, $r = 0.07$ (since 7% = 0.07), and $t = 6$.

Step2: Substitute the values into the formula

Substitute $P = 58280$, $r = 0.07$, and $t = 6$ into $V = P(1 - r)^t$:
$$V = 58280(1 - 0.07)^6$$
First, calculate $(1 - 0.07) = 0.93$. Then, calculate $0.93^6$.
$0.93^6 \approx 0.93\times0.93\times0.93\times0.93\times0.93\times0.93 \approx 0.646969$

Step3: Calculate the final value

Multiply $58280$ by $0.646969$:
$V \approx 58280\times0.646969 \approx 58280\times0.646969 \approx 37705.35$ (rounded to the nearest cent)

Answer:

$\$37705.35$