Chapter 2.4, Problem 43E

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

Chapter
Section

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

# We said that the logistic curve y = N 1 + A b − t is steepest when t = ln A ln b . Show that the corresponding value of y is N / 2 [HINT: Use the fact that ln A ln b = log b A .]

To determine

To prove: The value of the logistic curve y=N1+Abt at t=lnAlnb is N2.

Explanation

Given Information:

The provided logistic curve y=N1+Abâˆ’t is steepest at t=lnAlnb.

The value of the logistic curve y=N1+Abâˆ’t at t=lnAlnb is N2.

Formula used:

Logarithm base change property:

If a,b>0 and aâ‰ 1 then,

lnab=lnblna

Proof:

Consider the logistic curve y=N1+Abâˆ’t.

Substitute the value t=lnAlnb in y=N1+Abâˆ’t then calculate the value of the logistic curve,

y=N1+Abâˆ’t=N1+Abâˆ’lnA

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started