Question

the table shows two bacteria populations changing over time, measured in hours since the populations were first counted. time (hours) population a (millions) population b (millions) 0 12 64 1 6 48 2 3 36 1.5 27 describe a pattern for how each population changes from one hour to the next.

Explanation:

Step1: Analyze population A

For population A, when time $t = 0$, population is $12$ million. When $t=1$, it is $6$ million. $\frac{6}{12}=\frac{1}{2}$. When $t = 2$, population is $3$ million and $\frac{3}{6}=\frac{1}{2}$. When $t=3$, population is $1.5$ million and $\frac{1.5}{3}=\frac{1}{2}$. So population A is multiplied by $\frac{1}{2}$ each hour.

Step2: Analyze population B

For population B, when $t = 0$, population is $64$ million. When $t=1$, it is $48$ million. $\frac{48}{64}=\frac{3}{4}$. When $t = 2$, population is $36$ million and $\frac{36}{48}=\frac{3}{4}$. When $t=3$, population is $27$ million and $\frac{27}{36}=\frac{3}{4}$. So population B is multiplied by $\frac{3}{4}$ each hour.

Answer:

Population A is multiplied by $\frac{1}{2}$ each hour. Population B is multiplied by $\frac{3}{4}$ each hour.