Question

A population of bacteria doubles every 15 hours. Initially, the population of bacteria is 40.

Answer 1

Answer:

The population of the bacteria will be 254 after 40 hours

Step-by-step explanation:

Exponential Function

The exponential function can be expressed as

$f(x)=Cr^{kx}$

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

$f(x)=40.\ 2^{kx}$

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

$80=40.\ 2^{k(15)}$

It gives us

$2^{15k}=2$

Or, equivalently:

$15k=1$

$\displaystyle k=\frac{1}{15}$

The complete function is

$f(x)=40.\ 2^{x/15}$

Let's compute f(40):

$f(40)=40.\ 2^{40/15}$

$f(40)=40.\ 2^{2.667}$

$f(40)=40(6.35)$

$f(40)=254\ bacteria$

The population of the bacteria will be 254 after 40 hours