Posted by **Erica** on Thursday, January 6, 2011 at 9:58pm.

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

a) Find the initial population.

b) Write an exponential growth model for the bacteria population. Let t represent time in hours.

c) Use the model to determine the number of bacteria after 8 hours.

d) After how many hours will the bacteria count be 25,000?

Thank you!!

- Calc -
**Reiny**, Thursday, January 6, 2011 at 10:21pm
let the number be n

n = a e^(kt), where a is the initial number and t is the time in hours, k is a constant

case 1, when t=2, n = 125

125 = a e^2k

case 2 , when t = 4, n= 350

350 = a e^4k

divide the two equations

350/125 = a e^4k / (a e^(2k))

2.8 = e^2k

2k = ln 2.8

k = .5148

in first equation,

125 = a e^(2(.5148))

a = 44.64

a) so initially there were 46 bacteria.

b) n = 44.64 e^(.5148t)

c) when t = 8 , n = 44.64 e^(8(.5148)) = appr. 2744

d) 25000 = 44.64 e^(.5148 t)

560.0358 = e^ .5148t

.5148t = ln 560.0358

t = 12.29 hours

- Calc -
**Doody**, Thursday, April 26, 2012 at 12:13pm
lalalalalalalalalalalalalalalalalalalalala

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