A bacteria culture starts with 500 bacteria and doubles in size every 3 hours. How do you find an exponential model for t?

Solution:

Given, a bacteria culture starts with 500 bacteria and doubles in size every 3 hours.

We have to find an exponential model for t.

Let B be the amount of bacteria

At the beginning, B = 500

At the end of 3 hours, it will double

So, B = 2(500) = 1000

At the end of another 3 hours (6hrs), it will double again

So, B = 2(1000) = 2000

Using mathematical expression to represent the above exponential.

B =2^t/3(500)

We use t/3 so that we can calculate the amount of bacteria even if we have a portion of a 3-hour time period.

Therefore, the exponential model for t is B = 2^t/3(500).

A bacteria culture starts with 500 bacteria and doubles in size every 3 hours. How do you find an exponential model for t?

Summary:

A bacteria culture starts with 500 bacteria and doubles in size every 3 hours. An exponential model for t is B = 2^t/3(500).