**Problem XV**: A farmer releases 200 doodlebugs into his field. The population \( P \) of the doodlebugs is estimated by the model:\[P = \frac{1000}{1 + 3e^{-\frac{5t}{t+1}}}\]where \( t \) is the time in days.**Problem 19**: Find the time necessary for the population to increase to at least 2,000 doodlebugs.*Note*: This problem involves exponential growth modeling of a doodlebug population. To solve it, you need to determine the time \( t \) such that \( P \geq 2000 \).

Answered: XV. A farmer releases 200 doodlebugs…

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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XV. A farmer releases 200 doodlebugs into his field. The population P of the doodlebugs is estimated by the modelP = 1000 (1+3t), wheret is the time in days. 5 +t 19. Find the time necessary for the population to increase to at least 2000 doodlebugs.