   Chapter 4.6, Problem 42E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

# 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 S   = 50 ( 1   − e k t ) .During the first year, 8000 units were sold.(a) Solve for k in the model.(b) What is the saturation point for this product? (The saturation point is the limit of S as t → ∞ . ) (c) How many units will be sold after 5 years?(d) Use a graphing utility to graph the sales function.

(a)

To determine

To calculate: The value of k in model S=50(1ekt). Where model represents the sales 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 8000 units.

Explanation

Given Information:

The provided sales model is S=50(1ekt) and in the first year, the units of new product sold in the market was 8000 units.

Calculation:

Consider the sales equation S=50(1ekt).

The sale for the first year is 8000 units, means when t=1, S=8.

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

S=50(1ekt)8=50(1ek)1ek=850ek=1850

On further solve,

ek=1

(b)

To determine

To calculate: The saturation point for the new product in model S=50(1ekt). Where model represents the sales 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 8000 units. The saturation point when t

To determine

The number of units that will sold after 5 years by using the model S=50(1ekt). Where model represents the sales 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 8000 units.

To determine

To graph: The model S=50(1ekt) using the graphing calculator. Where model represents the sales 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 8000 units.

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