Answer:
4150 pheasants in the year 2105
Step-by-step 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
[tex]P(t)=a(1-r)^t[/tex]
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:
[tex]P(t)=4600(1-.017)^6[/tex]
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
[tex]P(t)=4600(.983)^6[/tex]
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.
