Answer:
<em>The population of the bacteria will be 254 after 40 hours</em>
Step-by-step explanation:
<u>Exponential Function</u>
The exponential function can be expressed as

Being C the initial value, r the ratio and k a real value.
We know the population of bacteria doubles every 15 hours. That gives us r=2. We'll use the value of 15 later.
We also know the population of bacteria is initially C=40. We can now set up the particular function

We can know that when x=15 hours, the population has doubled, i.e. f(15)=80, so

It gives us

Or, equivalently:


The complete function is

Let's compute f(40):




The population of the bacteria will be 254 after 40 hours