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A conservation organization releases 15 Florida panthers into a game preserve. After 2 years, there are 90 panthers in the preserve. The Florida preserve has a carrying capacity of 240 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.) 226 ✔ panthers 240 1 + 15e -1.0986t (c) When will the population reach 120? (Round your answer to two decimal places.) ✔ yr 2.46 (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 15 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.)

A conservation organization releases 15 Florida panthers into a game preserve. After 2 years, there are 90 panthers in the preserve. The Florida preserve has a carrying capacity of 240 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.) 226 ✔ panthers 240 1 + 15e -1.0986t (c) When will the population reach 120? (Round your answer to two decimal places.) ✔ yr 2.46 (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 15 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.)

Advanced Engineering Mathematics
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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A conservation organization releases 15 Florida panthers into a game preserve. After 2 years, there are 90 panthers in the preserve. The Florida preserve has a carrying capacity of 240 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 = 240 1 + 15e -1.0986t (b) Find the population after 5 years. (Round your answer to the nearest whole number.) 226 panthers (c) When will the population reach 120? (Round your answer to two decimal places.) 2.46 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 15 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
Transcribed Image Text:A conservation organization releases 15 Florida panthers into a game preserve. After 2 years, there are 90 panthers in the preserve. The Florida preserve has a carrying capacity of 240 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 = 240 1 + 15e -1.0986t (b) Find the population after 5 years. (Round your answer to the nearest whole number.) 226 panthers (c) When will the population reach 120? (Round your answer to two decimal places.) 2.46 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 15 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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