Question

A company charges a different shipping fee, depending on the weight of the item shipped. If the item shipped weighs 5 pounds or less, the shipping fee is the item's weight in pounds plus $3. For items that weigh more than 5 pounds, but less than or equal to 8 pounds, the shipping fee grows exponentially by a growth factor of 1.01. The company will not ship an item weighing more than 8 pounds.

Which piecewise function best models the shipping fee for an item weighing x pounds?

(1 point)

f(x)={5x+37.6(1.01)xifif0<x≤55<x≤8


f(x)={x+32.8(1.01)xifif0<x≤55<x≤8


f(x)={x+37.6(2.01)xifif0<x≤55<x≤8


f(x)={x+37.6(1.01)xifif0<x≤55<x≤8

Answer 1

f(x) = { x + 3, for 0 < x ≤ 5
8*(1.01)^(x−5), for 5 < x ≤ 8 }

Reason: up to 5 lb the fee is x+3. At 5 lb the fee is 8, and for heavier items the fee grows by factor 1.01 per pound, so start at 8 and multiply by 1.01^(x−5).