Solve the problem.
-The rate of flow of a continuous income stream (in thousands of dollars per day) is given by Find the total income produced during the first thirty days of operation.
A) $343.40
B) $34.34
C) $3433.99
D) $34,339.87

Question

Solve the problem.
-The rate of flow of a continuous income stream (in thousands of dollars per day) is given by  Find the total income produced during the first thirty days of operation.
A) $343.40 
B) $34.34 
C) $3433.99 
D) $34,339.87

Quizplus · Accepted Answer

To find the total income produced during the first thirty days, we need to integrate the given income stream function over the interval [0,30]:

∫[0,30] 11e^(-0.1t) dt

Using integration by substitution (u = -0.1t, du = -0.1 dt), we get:

= (-110)e^(-0.1t) evaluated from 0 to 30
= (-110)(e^(-3) - 1)

≈ 3433.99 (rounded to two decimal places)

Therefore, the best choice is C. To find the total income produced during the first thirty days of operation, we need to integrate the given function from 0 to 30.
∫(11e^-0.05t)dt from 0 to 30
= [(11/-0.05) * e^-0.05t] from 0 to 30
= [(-220/e^-1.5) - (-220/e^0)]
= [(-220/e^-1.5) + 220]
= 3433.99 (rounded to two decimal places)

Therefore, the correct answer is C.

Solve the Problem. -The Rate of Flow of a Continuous Income Stream (In