00:01
In this problem, we're told that the number of foxes in the particular region are growing at a rate of 7 % per year.
00:06
And we know that in 2010, there were 23 ,500 foxes.
00:10
So in part a, we want to find the function to model the population t years after 2010.
00:16
Well, because it's growing at a rate that is increasing by a percentage, we can use an exponential function.
00:22
So our general exponential function is f of t, so the amount of foxes after two years, will equal to f of zero, or f, sub 0, the initial amount, times 1 plus r, the rate, rates to the t power, where t is going to be the year since 2010.
00:40
So, let's go ahead and substitute in what we know.
00:42
Well, remember, f sub 0 is the initial amount.
00:45
And in 2010, there were 23 ,500 foxes.
00:48
So that would be our f sub zero value.
00:51
Now, for r, that's our rate.
00:53
But remember, we have to convert our percent to a decimal.
00:56
So we moved the decimal point two places to the left, so that will be 0 .07.
01:00
All raised to the t power.
01:02
Well, 1 plus 0 .07 is just 1 .07.
01:05
So we can write this simply as f of t equals 23 ,500 times 1 .07 raised to the t power.
01:14
So now we have our function.
01:16
In part b, what we want to do is to use our function to figure out the population in the year 2019.
01:22
Well, remember, t is the year since 2010.
01:25
Well, 2019 is nine years later.
01:28
So that means t is equal to nine.
01:29
So all we're going to do, is we're going to substitute 9 in place of t in our function.
01:37
So now we're at a point where we can go to our calculator.
01:40
And we type this in just as this.
01:41
So we're going to have 23 ,500, and then in parentheses, 1 .07, and for the exponent, we'll have a 9...