Question 1183096
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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
{{{P[n] = 1.2*P[n-1]}}}
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. 

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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 {{{P[n]}}}


So we end up with {{{P[n] = 40*(1.2)^n}}}


Let's try plugging in n = 0 and see what we get
{{{P[n] = 40*(1.2)^n}}}


{{{P[0] = 40*(1.2)^0}}}


{{{P[0] = 40*(1)}}}


{{{P[0] = 40}}}
So far, so good.


Now try n = 1
{{{P[n] = 40*(1.2)^n}}}


{{{P[1] = 40*(1.2)^1}}}


{{{P[1] = 40*(1.2)}}}


{{{P[1] = 48}}}
That works as well. So the answer is confirmed.
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