Answer:
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.
