My Math Forum question about exponential formula

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 January 22nd, 2017, 01:14 PM #1 Newbie   Joined: Jan 2017 From: cullowhee Posts: 1 Thanks: 0 question about exponential formula A population, P(t) (in millions) in year t, increases exponentially. Suppose P(9)=20 and P(eighteen)=29. a) Find a formula for the population in the form P(t)=ab^t Enter the values you found for a and b in your formula in the blanks below. Round your values to 4 decimal places. a= b=
January 22nd, 2017, 01:52 PM   #2
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Quote:
 Originally Posted by taytay A population, P(t) (in millions) in year t, increases exponentially. Suppose P(9)=20 and P(eighteen)=29. a) Find a formula for the population in the form P(t)=ab^t Enter the values you found for a and b in your formula in the blanks below. Round your values to 4 decimal places. a= b=
Start here:
$\displaystyle P(9) = ab^9 = 20$

$\displaystyle P(18 ) = ab^{18} = 29$

Now divide:
$\displaystyle \frac{ \text{P}(18 )}{ \text{P}(9) } = \frac{a b^{18} }{ a b^9} = \frac{29}{20}$

$\displaystyle b^9 = \frac{29}{20}$

Now you can find b. See what you can do from here to find a.

-Dan

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