Question

A music group expects to sell a new compact disc (CD) at the rate R(t)=20,000e−0.12t CDs per week, where t denotes the number of weeks since the CD was first released. To the nearest thousand, how many CDs are expected to be sold during the first 12 weeks after the release?

Answer 1

Answer:

4739 CDs

Step-by-step explanation:

Given the function that models the rate at which the disc is sold expressed as;

R(t)=20,000e^−0.12t

t is the number of weeks since the CD was first released

We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;

R(t)=20,000e^−0.12t

R(12)=20,000e^−0.12(12)

R(12)=20,000e^−1.44

R(12)=20,000(0.2369)

R(12) = 4738.56

Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs

Answer 2

Answer:

127,000

Step-by-step explanation:

you take the integral from 0 to 12 of R(t)