Question

Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day-from 5 to 10, then from 10 to 20, and so on. Is the population of bacteria a function of the number of days? If so, is it linear? Explain your reasoning.

Answer 1

The population of bacteria can be expressed as a function of number of days.

Population =
`\[5*2^(n-1)\]` where n is the number of days since the beginning.

Explanation:

Number of bacteria on the first day=
`\[5 * 2^(0) = 5\]`

Number of bacteria on the second day =
`\[5 * 2^(1) = 10\]`

Number of bacteria on the third day =
`\[5*2^(2) = 20\]`

Number of bacteria on the fourth day =
`\[5*2^(3) = 40\]`

As we can see , the number of bacteria on any given day is a function of the number of days n.

This expression can be expressed generally as
`\[5*2^(n-1)\]` where n is the number of days since the beginning.