What do I do in the next step?

Question

A city’s population, P (in thousands) can be modeled by the equation P x = 130(1.03)^x

Where x is the number of years after January 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?

is the equation 170,000=130(1.03)^x

then u would divide by 130? what would be next???

Answer choices: A: 8 B:9 C: 10 D:11

Answer 1

Yes, you are correct that you would divide by 130 first. However, since P is population in thousands, on the left side of the equation you should have 170, not 17,000. This leaves us with approximately:

1.31 = (1.03)^x

Now, if we take the log base 1.03 of both sides, we will just have x on the right side (becase log_n(n^x) = x), and the answer on the left:

log_1.03(1.31) = x

If you can just calculate this logarithm on a calculator for this class, you can plug this in and get your answer of approximately 9 years.

If your calculator doesn't allow a custom base for your log and you can only use ln, you will have to use the change of base formula:

log_1.03(1.31) = ln(1.31) / ln(1.03), and then solve that on your calculator, giving you the same answer of 9 years.