How long will it take for a culture of bacteria to increase from 1000 to 4000?

Question

Use the equation of, A=Pe^rt. Use K=0.657.

Answer 1

Let's break down what the formula represents:

A = Pe^rt

A: Final amount

P: Principal, or initial amount

r: exponential rate of growth (which I believe is also known as the growth rate or K)

t: time

From our given information, we know that:

A = 4000 bacteria

P = 1000 bacteria

r = 0.657

Plugging this in and solving for t, or the time it takes for the culture to increase from 1000 to 4000 bacteria:

A = Pe^rt

4000 = 1000e^0.657t (Plug in values for variables)

4 = e^0.657t (Divide by 1000)

ln 4 = ln e^0.657t (Apply natural logarithm to both sides to use logarithm properties and get rid of exponential)

ln 4 = 0.657t ln e

ln 4 = 0.657t

t = (ln 4)/0.657 (Solve for t)

Therefore, the time it takes for the culture to increase from 1000 to 4000 bacteria is 2.11.

The units will depend on the units of the growth rate, which is usually 1/hr. So I believe the answer is 2.11 hours.