A certain breed of mouse was introduced onto a small island with an initial population of 320 mice, and scientists estimate that the mouse population is doubling every year. 2.1. Find an exponential function P(t) that models the number of mice a�er t years. 2.2. Using your function estimate the mouse population a�er 8 years.
Accepted Solution
A:
Answer:1). [tex]P_{t}=320\times 2^{(t-1)}[/tex]2). 40960Step-by-step explanation:Initial population of the mouse has been given = 320The mouse population is doubling every year.So, population after one year = 320 × 2Population after second year = 320 × 2²Population after third year = 320 × 2³So the sequence formed is 320, 320×2, 320×4...........We can see population after every year is increasing exponentially with a common factor = [tex]\frac{320\times 2^{2} }{320\times 2}[/tex] = 2Part 1.Now we know the formula which models the population increase will be [tex]P_{t}=P_{0}r^{(t-1)}[/tex]Where [tex]P_{t}[/tex] = Population after t years and [tex]P_{0}[/tex] = Initial population[tex]P_{t}=320\times 2^{(t-1)}[/tex]Part 2. We have to calculate the value of [tex]P_{8}[/tex].[tex]P_{8}=320\times 2^{(8-1)}[/tex] = [tex]320\times 2^{7}[/tex] = 320 × 128 = 40960