SOLUTION: The number of bacteria N in a culture is given by the model N=250e^kt Where t is the time (in hours). If N=280 when T=10, estimate the time required for the population to d

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: The number of bacteria N in a culture is given by the model N=250e^kt Where t is the time (in hours). If N=280 when T=10, estimate the time required for the population to d      Log On


   

Question 170488: The number of bacteria N in a culture is given by the model
N=250e^kt
Where t is the time (in hours). If N=280 when T=10, estimate the time required for the population to double in size. Verify your estimate graphically.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
first, solve for k

280=250e^(10k) __ dividing by 250 __ 1.12=e^(10k)

taking natural log __ ln(1.12)=10k __ dividing by 10 __ (ln(1.12))/10=k

solve for doubling time __ 2=e^[(ln(1.12)/10)t]

taking natural log __ ln(2)=(ln(1.12)/10)t

dividing by (ln(1.12)/10) __ 10[(ln(2))/(ln(1.12)]=t __ 61.2=t (approx)