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Ostrovityanka [42]
4 years ago
9

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

Mathematics
1 answer:
Pepsi [2]4 years ago
6 0

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

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

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