Little Green Island originally had no turtles. After 55 turtles were introduced to the island eir population is modelled by N(t) = a × 2-t + 10, t ≥ 0 Where a is a constant and t is the time in years since the turtles were introduced. a) Find the value of a. b) Find the time, in years, for the population to decrease to 20 turtles. c) There is a number m beyond which the turtle population will not decrease. Find the value of m. Justify your answer.
Little Green Island originally had no turtles. After 55 turtles were introduced to the island eir population is modelled by N(t) = a × 2-t + 10, t ≥ 0 Where a is a constant and t is the time in years since the turtles were introduced. a) Find the value of a. b) Find the time, in years, for the population to decrease to 20 turtles. c) There is a number m beyond which the turtle population will not decrease. Find the value of m. Justify your answer.
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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![**1) Little Green Island originally had no turtles. After 55 turtles were introduced to the island, their population is modelled by**
\[ N(t) = a \times 2^{-t} + 10, \, t \geq 0 \]
**Where** \( a \) **is a constant and** \( t \) **is the time in years since the turtles were introduced.**
a) **Find the value of** \( a \).
b) **Find the time, in years, for the population to decrease to 20 turtles.**
c) **There is a number** \( m \) **beyond which the turtle population will not decrease.**
**Find the value of** \( m \). **Justify your answer.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd86db678-bc86-44fd-bd72-7c276c312ad6%2F1147f174-03c6-4673-a4c2-2f3dc52ff78c%2Ffsioabq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**1) Little Green Island originally had no turtles. After 55 turtles were introduced to the island, their population is modelled by**
\[ N(t) = a \times 2^{-t} + 10, \, t \geq 0 \]
**Where** \( a \) **is a constant and** \( t \) **is the time in years since the turtles were introduced.**
a) **Find the value of** \( a \).
b) **Find the time, in years, for the population to decrease to 20 turtles.**
c) **There is a number** \( m \) **beyond which the turtle population will not decrease.**
**Find the value of** \( m \). **Justify your answer.**
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