vation organization releases 35 Florida panthers into a game preserve. After 4 years, there are 204 panthers in the preserve. The Florida preserve has a carrying capac 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.) = (b) Find the population after 5 years. (Round your answer to the nearest whole number.) panthers c) When will the population reach 245? (Round your answer to two decimal places.)
vation organization releases 35 Florida panthers into a game preserve. After 4 years, there are 204 panthers in the preserve. The Florida preserve has a carrying capac 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.) = (b) Find the population after 5 years. (Round your answer to the nearest whole number.) panthers c) When will the population reach 245? (Round your answer to two decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A conservation organization releases 35 Florida panthers into a game preserve. After 4 years, there are 204 panthers in the preserve. The Florida preserve has a carrying capacity of 490 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.)
panthers
(c) When will the population reach 245? (Round your answer to two decimal places.)
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.)
dP
dt
P(5) ≈
(e) At what time is the panther population growing most rapidly? (Round your answer to two decimal places.)
yr
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