+23 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!
+128475 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
