   Chapter 6.2, Problem 57E ### 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
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# Population Growth In Exercises 57 and 58, use a graphing utility to graph the growth function. Use the integration table in Appendix C to find the average value of the growth function over the interval, where N is the size of a population and t is the time in days. N = 5000 1 + e 4.8 − 1.9 t ' [ 0 , 2 ]

To determine

To graph: The average value of growth function N=50001+e4.81.9t over the interval [0,2] using Appendix C. and then plot the graph of growth function over the interval [0,2] using graphic calculator.

Explanation

Given Information:

The growth function is;

N=50001+e4.81.9t

Graph:

Consider the provided function as:

Y1=N=50001+e4.81.9t

Graph the growth function N=50001+e4.81.9t over the interval [0,2] using graphic calculator Ti-83. The steps used to graph the provided growth function using graphic calculator Ti-84 are follow as:

Step 1: Press ON button and then press Y= button.

Step 2: Then, enter the function Y1=5000/(1+e(4.81.9t)).

Step 7: Now, press window button and set the window as Xmin=0, Xmax=10, Xscl=1, Ymin=0, Ymax=6000 and Yscl=1000.

Step 8: Press GRAPH button, to get the graph for the provided growth function.

The obtained graph for provided growth function N=50001+e4.81.9t is shown as:

Formula used:

The formula for the integral 11+eudu is;

11+eudu=uln(1+eu)+C

The Formula for average value of the function is;

average value=1baabf(x)dx

The General power differentiation Rule:

Calculation:

Consider the function u=4.81.9t.

Differentiate the considered function with respect to t using power rule of differentiation.

du=(01.9)dt=1.9dt

Consider the provided expression:

N=50001+e4.81.9t

Use the formula for average value to find the average value of growth function for interval [0,2].

average value=1200250001+e4

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