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.
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.
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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![**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 \( P \geq 2000 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92b9fa95-2e7d-446b-a380-41f972519da6%2Fcd21f626-e05f-4a7b-895e-08166bfe72ba%2Fnqxley4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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 \( P \geq 2000 \).
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