Problem: Using the doubling time growth model, what will the population for a city be in 4 years if the current

population is 750,000 and the doubling time is 36 years?

Step 1: What equation in terms of the variables Port and d would you use to solve this problem?

In four years the population will be 810,045 rounded to the nearest whole number.

Step-by-step explanation:

I'm not sure what port and d are but here's the solution.

since we know the doubling time we can set up a function where P is the initial value x will actually be the rate, since we know the time, which is what x usually is.

usually an exponential function looks like P*b^x=R where x is the time. We know the time though, 36 years. So we are going to use this to find the rate, which is normally b.

Px^36=2P

We don't need to worry about the actual values of P since we know that P gets doubled. Now we just use algebra to solve.

Px^36 = 2P

x^36 = 2

x = 2^ (1/36) or the thirty sixth root of 2, or about 1.019. So we know every year the population increases by about 1.9 percent. I am going to use 2^ (1/36) just to keep the answer accurate.

So now using the original equation we have P * (2^ (1/36)) ^x = R where now we can plug in any number for x and get what the population will be that many years after the start. Keep in mind it has to be years though, if you wanted anything longer or less than a year you'd have to convert something.

It asks for 4 years sowe just plug in 4 for x and of course 750,000 for P.

750,000 * (2^ (1/36)) ^4 = 810,045 if we round to the nearest whole number.

Also worth noting if you have something like (a^b) ^c you can rewrite it as a^ (bc) so the exponents multiply together. Just need to make sure c is a power to the whole term a^b.