SOLUTION: This exercise uses the population growth model. A culture starts with 8700 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: This exercise uses the population growth model. A culture starts with 8700 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n      Log On


   

Question 1026385: This exercise uses the population growth model.
A culture starts with 8700 bacteria. After 1 hour the count is 10,000.
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t) =

(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
_____bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
_____hr
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
p for population
x for time in hours
p=8700%2Ae%5E%28kx%29

Solve the model for k.
ln%28p%29=ln%288700%29%2Bkx%2Aln%28e%29
kx%2A1=ln%28p%29-ln%288700%29
k=%281%2Fx%29%28ln%28p%29-ln%288700%29%29

Substitute the point (1,10000).
k=%281%2F1%29%28ln%2810000%29-ln%288700%29%29
k=ln%2810000%29-ln%288700%29
k=0.13926-----which you might want only to three significant figures, or maybe just two.

If you want p after 2 hours, you could simply use 10000%2810000%2F8700%29 and it SHOULD be the same as 8700%2Ae%5E%280.139%2A2%29; just try it /them and see. The model more specifically is highlight%28p=8700%2Ae%5E%280.139%2Ax%29%29.

Find x for how long to double.
Take logs of both sides and solve for x.
More simply, 2=1%2Ae%5E%280.13926%2Ax%29---------start from this form.