the table shows two bacteria populations changing over time, measured in hours since the populations were…

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.

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.

Answer

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.