Calc
posted by Erica .
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
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
lalalalalalalalalalalalalalalalalalalalala
Respond to this Question
Similar Questions

Precalculus
NEED HELP ASAP PLEASE!! A bacteria culture starts with 2000 bacteria and the population doubles every 3 hours. a) A function that models the number of bacteria after t hours is p(t)=____________? 
MATH :)
3. In Biology, it is found that the bacteria in a certain culture double every halfhour. If the initial number of bacteria in culture is 1000, A. Find the defining equation for the number N of bacteria in culture after T hours, assuming … 
math
The number of bacteria in a culture is modeled by n(t)=1710e071t (a) The initial number of bacteria is (b) The relative rate of growth of this bacterium population is (c) The number of bacteria after 3 hours is (d) After how many hours … 
Math
he number of bacteria in a culture is modeled by n(t)=1710e071t (a) The initial number of bacteria is (b) The relative rate of growth of this bacterium population is (c) The number of bacteria after 3 hours is (d) After how many hours … 
math
The number of bacteria in a culture is modeled by: n(t) = 1330e^(0.42t) (a) The initial number of bacteria is: (b) The relative rate of growth of this bacterium population is: (c) The number of bacteria after 3 hours is: (d) After … 
College Algebra
The number of bacteria in a certain culture increased from 500 to 1000 between 7:00 A.M. and 9:00 A.M. Assuming growth is exponential, the number f(t) of bacteria t hours after 7:00 A.M. is given by f(t) = 500(2)^t/2. (a) Estimate … 
Calculus (math)
A bacteria culture grows with constant relative growth rate. The bacteria count was 784 after 2 hours and 117649 after 6 hours. What is the relative growth rate? 
Urgent math
population growth model. Can anybody please help me out in trying to solve this problem? 
algebra
the number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model at a relative rate of 6% per hour. suppose that a sample culture has an initial population of 94 bacteria. find … 
pre calc
The number N of bacteria in a culture at time t (in hours) grows exponentially according to the function N(t) = 1000e^0.01t. 1.What is the population after 4 hours?