Question

The value of a vase changes over time. When initially purchased, its value was $200. Its value declined exponentially at a decay factor of 0.8 for the next 4 years. Then for the next 6 years, its value increased at a rate of $50 each year.

Which piecewise function models the value of the vase x years after it is purchased?

(1 point)

f(x)={200(0.8)x50x−118.08ifif0≤x≤44<x≤10


f(x)={200(0.8)x50x+81.92ifif0≤x≤44<x≤10


f(x)={200(1.8)x50x+1899.52ifif0≤x≤44<x≤10


f(x)={200(0.8)x50xifif0≤x≤44<x≤10

Answer 1

f(x) = { 200(0.8)^x, 0 ≤ x ≤ 4
50x − 118.08, 4 < x ≤ 10 }

Reason: f(4)=200(0.8)^4 = 81.92, and for x>4 value grows by $50 per year so f(x)=81.92+50(x−4)=50x−118.08.