The current cost of a calculator is $70. Its value decreases by 7.5% each year.

Question

a. Write the exponential funciton that models this situation.

b. How much will the calculator be worth in 4 years?

c. How much was it worth 10 years ago?

Answer 1

since the price is decreasing by 7.5% each year ( that is 0.075) the function that models this situation

will be as follows 70 - 70(0.075) = 70(1-0.075) = 70(0.925) for each year  and for n years will be 70(0.925)^n

For 4 years later the calculator value will be 70(0.925)^4  =  70(0.7320) = 51.246 approx

we can consider this as a geometric progression having a rate of progress = 0.925

if consider the todays price of $70 as the a10 term of the progress (cause we must find the price of the calculator for ten years ago) then the first term would be a1. so the 10nth term a10 would be

a1(0.925)^10 = a10 = 70   -->>>  a1 = 70/0.925^10  = 70/0.45858  = 152.645 so its value 10 years ago

it was $152.645