A conservation organization releases 35 Florida panthers into a game preserve. After 2 years, there are 91 panthers in the preserve. The Florida preserve has a carrying capacity of 280 panthers. (a) Write a logistic equation that models the population of panthers in the preserve. (Round your k to four decimal places. Use t for the time in years.) P = (b) Find the population after 5 years. (Round your answer to the nearest whole number.) 210 panthers 280 1+7e-0.6075t (c) When will the population reach 140? (Round your answer to two decimal places.) 3.20 yr (d) Write a logistic differential equation that models the growth rate of the panther population. Then using Euler's Method, repeat part (b) with a step size of h = 1. Use the initial release population of 35 panthers as your initial value to start Euler's Method. (Round your answer to the nearest whole number.) 0.6075P 1- dP dt = P(5) 198 P 280 (e) At what time is the panther population growing most rapidly? (Round your answer to two decimal places.) 3.16 x vr

A conservation organization releases 35 Florida panthers into a game preserve. After 2 years, there are 91 panthers in the preserve. The Florida preserve has a carrying capacity of 280 panthers. (a) Write a logistic equation that models the population of panthers in the preserve. (Round your k to four decimal places. Use t for the time in years.) P = (b) Find the population after 5 years. (Round your answer to the nearest whole number.) 210 panthers 280 1+7e-0.6075t (c) When will the population reach 140? (Round your answer to two decimal places.) 3.20 yr (d) Write a logistic differential equation that models the growth rate of the panther population. Then using Euler's Method, repeat part (b) with a step size of h = 1. Use the initial release population of 35 panthers as your initial value to start Euler's Method. (Round your answer to the nearest whole number.) 0.6075P 1- dP dt = P(5) 198 P 280 (e) At what time is the panther population growing most rapidly? (Round your answer to two decimal places.) 3.16 x vr

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.2: Applications Of Exponential Functions

Problem 34E

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