Calculus

posted by Ben Klotz

Suppose bacteria is growing on a pizza that has been taken out of the refrigerator at a rate that is proportional to the number of bacteria. Suppose there were 50 bacteria when the pizza was removed from the refrigerator and one hour later there were 200 bacteria. How many bacteria would there be 6 hours after the pizza was removed from the refrigerator?

1. Steve

first, it's "bacteria are" growing.

You are told that the for a population p of these bacteria,

dp/dt = kp
so, that means that

dp/p = k dt
ln p = kt + c
p(t) = c e^(kt)

p(0) = c = 50
So,

p(t) = 50e^(kt)

p(1) = 200, so
50e^k = 200
k = ln 4

p(t) = 50e^(ln4 t)
Or, since it is clear that the population quadruples every hour, (and since e^ln4 = 4):

p(t) = 50*4^t

So, now find p(6)

Similar Questions

1. Calculus

Suppose that a population of bacteria triples every hour and starts with 700 bacteria. (a) Find an expression for the number n of bacteria after t hours. n(t) = ?
2. math modeling

At 3a.m., there is a colony of 736 bacteria, and it is growing at a continuous hourly rate of 10.77%. How many bacteria are there at 7p.m.?
3. chemistry

Suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 °C: TIme (s) number of bacteria 0 100 19 200 38 400 57 800 76 1600 what is the rate order?
4. calculus

2. The rate of change in the number of bacteria in a culture is proportional to the number present. In a certain laboratory experiment, a culture has 10,000 bacterial initially, 20,000 bacteria at time t1 minutes, and 100,000 bacteria …
5. Chem

suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 °C: t (min):0 15.0 30.0 45.0 60.0 Number of bacteria: 100 200 400 800 1600 What is the order …
6. math

Bladder infections are often caused when the bacteria E. coli reach the human bladder. Suppose that 3000 of the bacteria are present at time t = 0. Then t minutes later, the number of bacteria present will be a) How many bacteria will …
7. Math

A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later. Find the rate of growth, …
8. Math

A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later. How many bacteria …
9. math

The rate of increase of bacteria in a culture is proportional to the number of bacteria present .if the original number of bacteria double in the two hours, in how many hours will it be five times?
10. Calculus

I just need help with one question. A bacteria population starts with 500 bacteria and grows at a rate of r(t) = 548e^(6.5t) bacteria per hour. Determine the number of bacteria after 1 hour. Thank you!

More Similar Questions