jess wants to buy a car but she cannot decide if she should buy a Honda or a Kia. The Honda costs $16,000 and depreciates at an annual rate of 8%. The Kia costs $12,000 and depreciates at an annual rate of 12%. What will each car be worth in 5 years? In 10 years? Which car should she buy and why?

Step-by-step explanation:

Honda : 16,000

each year depreciates 8% from 100% so will be left with 100-8 =92% or 0.92

in 5 years : 16,000* 0.92^5 ≈ $10,545.30

in 10 years : 16,000* 0.92^10 ≈ $6,950.22

Kia : $12,000

each year depreciates 12 % from 100% so will be left with 100-12 =88% or 0.88

in 5 years : 12,000* 0.88^5 ≈ $6,332.78

in 10 years : 12,000* 0.88^10 ≈ $3,342.01

Jess should buy the Honda if wants to use it for 5 years or less because although is more expensive than Kia, it depreciates less in 5 years.

In 5 years the difference in depreciation is 10,545.30 -6,332.78= $ 4,212.52 this is greater that the difference in the actual price 16,000-12,000 =$ 4,000

Jess should buy the Kia if wants to use the car for 10 years or more because Kia will depreciates less than Honda in 10 years.

In 10 years the difference in depreciation is 6,950.22 -3,342.01 =$ 3, 608.21 this is lower that the difference in the actual price 16,000-12,000 =$ 4,000

graph #4 (last graph) depict the function   f(x)= -m(x-d)^1/5 i

step-by-step explanation:

we know that

m=slope

but in this function slope is -m that means slope is decreasing and it is decreasing by 1/5 points down the x-axis.

which is shown in graph four

a decreasing slope down x-axis by 1/5 points.

hence 4th graph is the right option for this.