Acertain 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.

Exponential functions are often used to model population.

The given parameters are:

--- initial population

-- rate

(a) The exponential function

This is calculated as:

Substitute known values

(b) The population after 8 years

This means that t = 8.

So, we have:

Hence, the mouse population after 8 years is 40960

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1).

2). 40960

Step-by-step explanation:

Initial population of the mouse has been given = 320

The mouse population is doubling every year.

So, population after one year = 320 ×  2

Population after second year = 320 × 2²

Population after third year = 320 × 2³

So the sequence formed is 320, 320×2, 320×4...........

We can see population after every year is increasing exponentially with a common factor = = 2

Part 1.

Now we know the formula which models the population increase will be

Where = Population after t years

and = Initial population

Part 2.

We have to calculate the value of .

               =

               = 320 × 128

               = 40960