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# Super important!!!

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Andre observes that the population of a species grows exponentially over time. Initially, there are 120 organisms of the species. After 6 days, the population grows to 180 organisms.

How many days until the population of the species is 500 organisms? Round your answer to the nearest whole number.

I got 32 as the answer, let me know if I'm wrong!

Dec 19, 2019

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We have this  form

P = ab^t        where P  is the population after t days  and a  = 120

So  we have

180  =  120 b^(6)     divide both sides by  120

1.5  =   b^6               take the 6th root of both sides

(1.5)^(1/6)  =  b

And we want   to  know

500  =   120 * [1.5^(1/6) ] ^ t      divide both sides by 120

25/6  =  [ 1.5^(1/6) ]^t            take the log of both sides

log (25/6)  = log  [ 1.5^(1/6)]  ^t           and we can write

log (25/6) = t * log [1.5 ^(1/6) ]       divide both sides by  log [ 1.5^(1/6) ]

log (25/6)  /log [ 1.5^(1/6) ]  = t ≈   21   days   Dec 19, 2019