Question

During the exponential phase, E. coli bacteria in a cultureincrease in number at a rate proportional to the currentpopulation. If the growth rate is 1.9% per minute and thecurrent population is 172.0 million, what will thepopulation be 7.2 minutes from now?

Answer 1

Case: Exponential case

General model:

After time x, the number will be:

`y=a(b)^x`

where a is the initial value and

b is the growth or multiplier rate

Method:

Since the growth rate is 1.9% per minute,

the current population is 172.0 million.

Here:

a= 172.0 million

b= 1.9% or 1.019

Find the number of E coli bacteria if the time x is 7.2 minutes

`\begin{gathered} y=172.0(1.019)^(7.2) \\ y=196.962 \end{gathered}`

Final answer:

The population 7.2 minutes from now will be:

196.962 million