How do I set this up?
The initial value of a car is 25,000. After one year, the value of the car is 21,250. Write an exponential function to model the expected value of the car. Estimate the value of the car after 5 years.

Question

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

What is the change in price from 25,000 to 21,250

anonymous · Answer

3,750

jim_thompson5910 · Answer

divide that by the initial price to get ?

anonymous · Answer

6 2/3

anonymous · Answer

y(t) = Y(0) k^t

21250 = 25000 k^1

k = 0.85

y(t) = 25000 (0.85)^t

y(5) = 25000(0.85)^5 = 11093

value is declining 15% per year (k=0.85)

anonymous · Answer

got 0.85 from the ratio of the price after one year to the initial price, did
this because "exponential function" hint indicates that ratios are key rather than absolute differences.

Value is declining 15% per year, same as multiplying by 0.85 year after year.

anonymous · Answer

Well I understand the 0.85 but not exactly sure about the 15% still

jim_thompson5910 · Answer

the 85% or 0.85 comes from 100% - 15% = 85%

anonymous · Answer

Oh okay.

anonymous · Answer

Thank you both!

anonymous · Answer

You are quite welcome.

jim_thompson5910 · Answer

btw, you divided in the wrong order and it should be

3750/25000 = 0.15

so that represents a 15% decrease in value