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

Answer:

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.

Step-by-step 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.