Calculus 2 question

Question

A bacterial culture has an initial population of 10,000. If its population declines to 4000 in 6 hours, 6) when will its population be 2947? Assume that the population decreases according to the

exponential model.

Answer 1

General equation looks like P(t) = P(0)e^-kt where P(0) is the initial population, t is time, and k is a constant we must find.

at t = 6, we have P(6) = 10,000*e^-6k = 4000

e^-6k = 4/10

using logarithms we have:

-6k = ln(.4) −−» k = -ln(.4)/6 (don't use your calculator yet!)

Finally we have:

2947 = 10000*e^-kt

using logs again:

-kt = ln(2947/10000) −−» t = 6*ln(2947/10000)/ln(.4) (make sure to verify all steps on paper!)

t ≅ 8

As you can see, you need to be comfortable working with logarithms to succeed on these questions. Keep at it!