Chapter 6, Problem 33RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Sales The sales S (in thousands of units) of a new product after it has been on the market for t years is given by S = C e k / t .(a) Find S as a function of t when 5000 units have been sold after 1 year and the saturation point for the market is 30,000 units (that is, lim t → ∞ S = 30 ).(b) How many units will have been sold after 5 years?

(a)

To determine

To calculate: The sales(in thousands of units) of a new product as a function of time tS=Cekt if for t=1,S=5 and saturation point of the market is 30000limtS=30000

Explanation

Given: t=1,S=5 and limtâ†’âˆžS=30000

Formula used:

The sales model S=Cekt

Here S is the sales,t is time in years and C is the sales at t=âˆž.

Calculation:

Consider the expression S=Cekt â€¦â€¦ (1)

Now, it is given that when t=1 then S=5

So, put the above values in equation 1:

S=Cekt5=Cek1C=5ekâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰

(b)

To determine

To calculate: The no. of units that will have been sold after 5 years

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