SOLUTION: A culture contains 10 000 bacteria, and grows at a rate of 15% per hour. a) Write an equation expressing the population, P in thousands as a function of n, the time in hours.

Question 177046: A culture contains 10 000 bacteria, and grows at a rate of 15% per hour.
a) Write an equation expressing the population, P in thousands as a function of n, the time in hours.
b) Solve your equation from part a) for n

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A culture contains 10 000 bacteria, and grows at a rate of 15% per hour.
;
a) Write an equation expressing the population, P in thousands as a function of n, the time in hours.
P(n) = Ao*(1.15^n)
where
P = amt after n hrs (in thousands)
Ao = initial amt (in thousands)
n = time in hrs
;
b) Solve your equation from part a) for n
10*(1.15^n) = P
1.15^n =
log(1.15^n) = log(.1P)
:
.0607n = log(.1P)
n =
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