Question

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?

Answer 1

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.

Answer 2

The equation will be $\rm P' = 750000*(1.01944)^x$ and the population of the city after four years is 810,045.

What is an exponent?

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

Using the doubling time growth model, the population for a city is in 4 years.

If the current population is 750,000 and the doubling time is 36 years.

Let the P be the initial value x will be the actually be the rate.

Then the exponent function will be

$\rm P*x^{36} = 2P$

Then the value of x will be.

$\begin{aligned} \rm x^{36} &= 2 \\\\ x  &= 2^{\frac{1}{36}} \\\\ x &= 1.01944 \end{aligned}$

Then the population P' in 4 years will be

$\rm P' = 750000*(1.01944)^{4} \\\\ P' = 810045$

Thus, the equation will be $\rm P' = P*(1.01944)^x$, and the population of the city after four years is 810,045.

More about the exponent link is given below.

https://brainly.com/question/5497425