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

To find the total income from years 3 through 5, we need to integrate the given function from t=36 (3 years = 36 months) to t=60 (5 years = 60 months), and then multiply by 12 to get the annual income.

∫11e^(0.06t) dt [from t=36 to t=60] = (11/0.06) [e^(0.06t)] from t=36 to t=60
= (11/0.06) [e^(0.06*60) - e^(0.06*36)]
= 1,684,306.74 (rounded to the nearest penny)

Multiplying by 12, we get the annual income: $20,211,680.88.

Therefore, the best choice is D, which matches the answer we obtained.

Suppose That the Carter Car Service Franchise Finds That the Income