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100 · f'(x) f(x) The relative rate of change of a differentiable function y = f(x) is given by %. One model for population growth is a Gompertz growth function, given by P(x) = ae-b where a, b, and c are constants. (a) Find the relative rate of change formula for the generic Gompertz function. (b) Use part (a) to find the relative rate of change of a population in x = 20 months when a = 205, b = 0.0197, and c = 0.15. (Round your answer to five decimal places.)

100 · f'(x) f(x) The relative rate of change of a differentiable function y = f(x) is given by %. One model for population growth is a Gompertz growth function, given by P(x) = ae-b where a, b, and c are constants. (a) Find the relative rate of change formula for the generic Gompertz function. (b) Use part (a) to find the relative rate of change of a population in x = 20 months when a = 205, b = 0.0197, and c = 0.15. (Round your answer to five decimal places.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Relative Rate of Change and the Gompertz Function** The relative rate of change of a differentiable function \( y = f(x) \) is given by: \[ \frac{100 \cdot f'(x)}{f(x)} \% \] One model for population growth is a Gompertz growth function, defined by: \[ P(x) = ae^{-b \cdot e^{-cx}} \] where \( a, b, \) and \( c \) are constants. ### (a) Task: Find the relative rate of change formula for the generic Gompertz function. [Input Box] ### (b) Task: Use the formula from part (a) to find the relative rate of change of a population at \( x = 20 \) months given the parameters \( a = 205 \), \( b = 0.0197 \), and \( c = 0.15 \). Round your answer to five decimal places. [Input Box with a placeholder: %]
Transcribed Image Text:**Relative Rate of Change and the Gompertz Function** The relative rate of change of a differentiable function \( y = f(x) \) is given by: \[ \frac{100 \cdot f'(x)}{f(x)} \% \] One model for population growth is a Gompertz growth function, defined by: \[ P(x) = ae^{-b \cdot e^{-cx}} \] where \( a, b, \) and \( c \) are constants. ### (a) Task: Find the relative rate of change formula for the generic Gompertz function. [Input Box] ### (b) Task: Use the formula from part (a) to find the relative rate of change of a population at \( x = 20 \) months given the parameters \( a = 205 \), \( b = 0.0197 \), and \( c = 0.15 \). Round your answer to five decimal places. [Input Box with a placeholder: %]
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