Question

A car was purchased for $3,495 and will depreciate 20% each year.

Find a linear function for the value of the car at time t in years. Define variables clearly.
Graph the function you found in part A. A claim is made that the car will not be worth anything in five years. Do you agree with this claim? Explain. In your explanation include the following:
State the problem in your own words. Describe the strategy used to solve the problem. Clearly state your answer and explain why it is reasonable.
Tell whether you agree with the claim, explaining why or why not

Answer 1

The original purchase price is $3,495. It decreases by 20% each year. This means that for the next year it would be:

$3495 - 0.2($3495) = $2796

If this pattern goes on, the equation would be $3495(1-0.2)^n, where n is the number of years. Simplifying the equation, it would be 3495*0.8^n. Equate this to y which is the purchase price at year n. To graph this, assign values for n. The output would be as shown in the attached image.

After 5 years, a claim said that its worth would be nothing. This is false. Based on the graph created, at year 5 (n = 5), the purchase price is worth $1145. To find how many years would its worth be nothing, you could solve this:

y = 3495*0.8^n
0 = 3495*0.8^n
n = 40

Hence, it would take 40 years which is way too early for 5 years.