Suppose that the Carter Car Service franchise finds that the income generated by its stores can be modeled by assuming that the income is a continuous stream with a monthly rate of flow at time t given by (dollars per month). Find the total income from a Carter Car Service store for years 3 through 5 of operation and round to the nearest penny.
A) $973,587.71
B) $2,307,500.23
C) $1,059,312.41
D) $1,684,306.74
E) $1,186,131.50

Question

Suppose that the Carter Car Service franchise finds that the income generated by its stores can be modeled by assuming that the income is a continuous stream with a monthly rate of flow at time t given by  (dollars per month). Find the total income from a Carter Car Service store for years 3 through 5 of operation and round to the nearest penny. ​
A) $973,587.71 
B) $2,307,500.23 
C) $1,059,312.41 
D) $1,684,306.74 
E) $1,186,131.50

Quizplus · Accepted Answer

We need to find the total income generated by a Carter Car Service store from year 3 to year 5, which is the same as finding the definite integral of the given rate function from t=36 to t=60.

So,

Total income =  ∫(36 to 60) 11e^(0.01t) dt

Using integration by substitution, let u = 0.01t, then du/dt = 0.01, and dt = du/0.01.

So,

Total income = 11/0.01 ∫ e^u du   (substituting the limits from u = 0.36 to u = 0.60)

Total income = (1100/0.01) [ e^0.60 - e^0.36 ]

Total income ≈ $1,684,306.74

Therefore, the best choice is D.

Suppose That the Carter Car Service Franchise Finds That the Income