Explanation Given information: y = a 1 + b e − t ; y-intercept =2; inflection point at t = 1. Definition used: A point at which the graph of a function f changes concavity is called an inflection point. At the inflection points, f ' ' is zero or undefined. Calculation: y = a 1 + b e − t (Given) y = a ( 1 + b e − t ) − 1 Differentiating with respect to ‘t’, we get y ' = a ( − 1 ) ( 1 + b e − t ) − 2 ( − b e − t ) = a b e − t ( 1 + b e − t ) − 2 y ' ' = a b [ ( − e − t ) ( 1 + b e − t ) − 2 + e − t ( − 2 ) ( 1 + b e − t ) − 2 − 1 ( − b e − t ) ] = a b e − t ( 1 + b e − t ) 2 ( − 1 + 2 b e − t ( 1 + b e − t ) − 1 ) = a b <

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4.2, Problem 40P

To determine

To find:

Formula for the function y=a1+be−t with y-intercept 2 and an inflection point at t=1.

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Chapter 4.2, Problem 39P

Chapter 4.2, Problem 41P

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Chapter 4 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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Formula for the function y = a 1 + b e − t with y-intercept 2 and an inflection point at t = 1.

Solution Summary: The author explains the formula for the function y=a1+be-t.

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To find:

Formula for the function y=a1+be−t with y-intercept 2 and an inflection point at t=1.

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Chapter 4 Solutions

Formula for the function y = a 1 + b e − t with y-intercept 2 and an inflection point at t = 1.

Solution Summary: The author explains the formula for the function y=a1+be-t.

Concept explainers

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To find: Formula for the function y=a1+be−t with y-intercept 2 and an inflection point at t=1.

Want to see the full answer?

Chapter 4 Solutions

To find:

Formula for the function y=a1+be−t with y-intercept 2 and an inflection point at t=1.