At the beginning of a study, a certain culture of bacteria has a population of 40. The population grows according to a continuous exponential growth model. After 6 days, there are 124 bacteria.

Answer 1

If you are looking for the rate that the bacteria grows then start with the basic equation for exponential growth:

A(t) = A₀(1 + r)^t where "A(t)" is (in this case) the number of bacteria at any time "t", A₀ is the number of bacteria at the beginning (or at time zero), and "r" is the rate they are growing.

Since we know A(6) = 124 and A₀ = 40, we can say:

124 = 40(1 + r)⁶

124/40 = (1 + r)⁶

3.1 = (1 + r)⁶

⁶√(3.1) = ⁶√((1 + r)⁶)

1.2075 = 1 + r

r = 1.2075 - 1

r = 0.2075

Typically we would turn that into a percent by multiplying it by 100 to get

r = 20.75%

If you were looking for the equation that would model this situation, it would then be:

A(t) = 40(1.2075)^t