In the year 2000, the estimated population of Canadian geese in a city was 750. The Canadian geese population is expected to grow at a rate of 12% each year. In what year will the population first exceed 15,000?

Question

mathstudent55 · Answer

You need to start with the equation for exponential growth.
Do you know it?
If you don't know it, try looking it up and write it.

freemap · Answer

d/n / d/t = r

mathstudent55 · Answer

$y = P_i(1 + r)^x$

y = population at year x
$P_i$ = initial population
r = rate of growth (written as a decimal)
x = year

mathstudent55 · Answer

You know the future population, y = 12,000

You also know r = 12%, and $P_i $ = 750.

The only unknown is x, the number of years.

freemap · Answer

12,000 =750(1+12)^x

freemap · Answer

133 years?

mathstudent55 · Answer

No. It's a much smaller number.
I noticed I made a mistake, though. The future population is 15,000, not 12,000 as I wrote above.
Also, you need to convert 12% to a decimal.
12% = 0.12

This is the equation you need to solve.

$15,000 = 750(1.12)^x$

First, divide both sides by 750.
Then use logs to find x.

freemap · Answer

18

mathstudent55 · Answer

No. I don't get 18.
Divide both sides by 750 to get this.
Now take log of both sides.
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