Thread: Exponential Growth.

Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in a culture after t hours, and suppose that P(t) satisfies the differential equation .

1) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 100,000.
2) What is the size of the bacteria culture when it is growing at the rate of 34,000 bacteria per hour?

I have problems with setting the equation up. Thanks in advance!

Originally Posted by Affinity

Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in a culture after t hours, and suppose that P(t) satisfies the differential equation .

1) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 100,000.
2) What is the size of the bacteria culture when it is growing at the rate of 34,000 bacteria per hour?

I have problems with setting the equation up. Thanks in advance!

P(t) is the population at time t.
P'(t) is the rate of population change.

1) P(t) = 10000, so P'(t) = 0.55*100000 = 55000 bacteria/hr.

2) P'(t) = 34000 so
34000 = 0.55*P(t)

P(t) = 34000/0.55 = 61818 bacteria (or so)

-Dan