Find the total income from the machines over the first 3 years

Question

Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by

f(t) = 180e^0.07t

in thousands of dollars per year. Find the total income from the machines over the first 3 years

Answer 1

Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by

f(t) = 180e^0.07t

in thousands of dollars per year. Find the total income from the machines over the first 3 years

SOLUTION

Total Income = ∫₀³ 180 e^0.07t d t = 180 ∫₀³ e^0.07t d t

( 180/ 0.07) e^0.07t |₀³ = ( 18000/7) [ e^0.21 − e⁰ ] = 600. 88 thousands of dollars ^

Answer 2

Total income of machine over 3 _{years= 180*e^.04*3 = 202.94thousand dollars per year}