Question

The pheasant population on an island is declining at a rate of 1.7%per year.the population was 4600 in the year 2009.what is the best prediction of the population in the year 2015

Answer 1

4150

Explanation:

took the test and got it correct

Answer 2

4150 pheasants in the year 2105

Explanation:

First thing we are going to do is define the years. We will call year 2009 our year t = 0. Therefore, year 2015 is t = 6.

The decay equation that we need has a standard form of

`P(t)=a(1-r)^t`

where P(t) is the ending population after a certain amount of time goes by, a is the initial population at t = 0, r is the rate in decimal form, and t is time in years. Fitting in our info gives us a standard form equation that looks like this:

`P(t)=4600(1-.017)^6`

This means that we are looking for the ending population at a rate of decay of 1.7% after 6 years have gone by.

Doing the subtraction in the parenthesis first simplifies it down a bit to

`P(t)=4600(.983)^6`

Raise .983 to the 6th power to get

P(t) = 4600(.9022379843)

and then multiply to get

P(t) = 4150

This means that in the year 2015 the population of pheasants is 4150, dropping from 4600 six years earlier.