   Chapter 2.4, Problem 43E

Chapter
Section
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+Abt is steepest at t=lnAlnb.

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

Formula used:

Logarithm base change property:

If a,b>0 and a1 then,

lnab=lnblna

Proof:

Consider the logistic curve y=N1+Abt.

Substitute the value t=lnAlnb in y=N1+Abt then calculate the value of the logistic curve,

y=N1+Abt=N1+AblnA

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