Question

Chris is a researcher at the Centers for Disease Control and Prevention, and he is trying to understand the behavior of a new

and dangerous virus. He starts his experiment with 25 viruses that grow at a rate of 75% per hour. He will check on the
viruses in 12 hours. How many viruses will he find? Round your answer to the nearest whole number.

Answer 1

Answer:202,577 viruses

Answer 2

Chris will find 20625 viruses in 12 hours

Explanation:

Geometric Progressions

The geometric progression can be understood as a sequence or ordered terms when the term n equals the previous term n-1 by a constant value called the common ratio

`a_n=a_(n-1)r`

Recursively going back we find that

`a_n=a_1r^n`

Being
`a_1` the first term of the sequence

Chris' experiment shows that viruses grow at a rate of 75% per hour. It means that we get the next generation of viruses as the previous by 1.75. This is the common ratio. We also know he starts his experiment with 25 viruses, this makes

`a_1=25\ ,\ r=1.75`

We can now express the number of viruses as a function of the number of hours n:

`a_n=25\left ( 1.75 \right )^n`

We are required to compute the number of viruses found when n=12 hours:

`a_(12)=25\left ( 1.75 \right )^(12)`

`a_(12)=25(825)`

`a_(12)=20625 \ viruses`