Question

1. what is the initial resale price?
2. what is the factor from one resale price to the next?
3. write the equation for this exponential relationship.

Explanation:

Step1: Find initial resale price

The initial price is at year 0: $\$80,000$

Step2: Calculate the common factor

Divide price at year 1 by year 0: $\frac{40}{80} = 0.5$
Verify with year 2/year1: $\frac{20}{40} = 0.5$

Step3: Write exponential equation

Use form $P(t) = P_0 \times r^t$, where $P_0=80$, $r=0.5$: $P(t) = 80(0.5)^t$

Answer:

1. $\$80,000$
2. $0.5$
3. $P(t) = 80(0.5)^t$ where $P(t)$ is the resale price in thousands of dollars and $t$ is the number of years.