00:01
In this question, we are told that the population of a city is given is 25 ,000 in 1970, 30 ,000 in 1980.
00:09
And we are asked to approximate the population in 2010.
00:14
So we'll let p of 0 be 25 ,000, which is the population in 1970.
00:20
P of 10 equals 30 ,000 is the population in 1980.
00:26
And then we need to calculate p of 40, because 2010 is 40 years after 1970.
00:34
We are asked to use the exponential model, which means p of t equals a multiplied by b to the power of t.
00:42
Or we can also rewrite this as a multiplied by e to the rt, where r is the rate of growth.
00:51
And now, well, you can use either of these formulas.
00:54
They're equivalent.
00:56
I'll use this formula.
00:58
And i'll use the given conditions to find the constants a and r.
01:05
P of 0 equals 25 ,000.
01:08
On the other hand, if we plug in t equals 0 in this formula, we'll get a multiplied by e to the 0, and that's just a.
01:16
So we found the value of a.
01:19
P of t now equals 25 ,000 times e to the rt.
01:26
Now we need to find the value of r.
01:29
To do that, we'll use the p of 10 condition...