Question

Bacteria colonies can triple in size every 4 days. If you start with 40 bacteria microorganisms, how large would the colony be after 20 days? First, complete the equation: Future Amount = 40(1 + [?])0

Answer 1

Exponential Growth

Some real-life events grow in such a way that they can be modeled as an exponential function, given as:

`C(t)=C_o(1+r)^t`

Where C(t) is the future value of the measured variable, Co is its initial value, r is the growth rate and t is the time.

We are given the following data:

Initial amount: Co=40 bacteria

Growth rate: 1 + r = 3

The bacteria triples every 4 days, thus t is the number of periods of 4 days.

Thus the model is:

`C(t)=40(3)^t`

We can solve the equation

1 + r = 3

And get r = 2. Rewriting the equation:

`C(t)=40(1+2)^t`

We are required to find the number of bacteria after 20 days, that is, after 20/4 = 5 periods of 4 days. Substituting:

`C(5)=40(3)^5`

Calculating:

`C(5)=40\cdot243=9,720`

The colony would have 9,720 bacteria after 20 days