SOLUTION: Having trouble using the example already posted on this site to solve this equation, please help. A population grows according to an exponential growth model, with P0=40 and P1=

Question 1183096: Having trouble using the example already posted on this site to solve this equation, please help.
A population grows according to an exponential growth model, with P0=40 and P1=48
Complete the recursive formula:
Pn = ×Pn−1
Write an explicit formula for Pn
Pn =
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

P0 is the first population value, and it's 40
P1 is the second population value, and it's 48
Dividing the values gets us P1/P0 = 48/40 = 1.2

So we can say

meaning: "to get the current population, we multiply the previous population by 1.2"

This wraps up the recursive formula. As with any recursion problem, don't forget to mention the starting value.
-------------------------------------------------------

Now onto the explicit formula.

We found that 1.2 is the multiplier from the last section. This is the value of b in y = a*b^x

The value of 'a' is the starting value, so a = 40

So we have y = a*b^x update to y = 40*(1.2)^x

Then we'll replace x with n, and replace y with

So we end up with

Let's try plugging in n = 0 and see what we get

So far, so good.

Now try n = 1

That works as well. So the answer is confirmed.

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