Chapter 4.6, Problem 41E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Sales** The cumulative sales *S* (in thousands of units) of a new product after it has been on the market for *t* years are modeled by

During the first year, 5000 units were sold. The saturation point for the market is 30,000 units. That is, the limit of *S* as

(a) Solve for C and *k* in the model.

(b) How many units will be sold after 5 years?

(c) Use a graphing utility to graph the sales function.

**(a).**

To determine

**To calculate:** The value of *C* and *k* in model *S* (in thousands of units) of a new product after, it is in the market for t number of years. If in the first year, the units of new product sold in the market were

Explanation

**Given Information:**

The provided sales model is

**Calculation:**

Consider the sales equation

The sale for the first year is

Substituting the values of S and t in the provided model,

Now, sales is

Substituting the values,

Apply the limit as

Substitute the value of

**(b)**

To determine

The number of units that will sold after *S* (in thousands of units) of a new product after, it is in the market for t number of years. If in the first year, the units of new product sold in the market was

**(c)**

To determine

**To graph:** The model *S* (in thousands of units) of a new product after, it is in the market for t number of years. If in the first year, the units of new product sold in the market was

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