Question

the table below represents a type of bacteria that doubles every day and a half. a petri dish starts out with 12 of these bacteria.

days (x)	amount of bacteria (f(x))
1	19
2	30
3	48
4	76
5	121
6	192

calculate the average rate of change for the function between day 2 and day 6
3 bacteria per day
30 bacteria per day
40.5 bacteria per day
0.025 bacteria per day

Explanation:

Step1: Recall average rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, $f(2)=30$, and $f(6)=192$.

Step2: Substitute values into formula

$\frac{f(6)-f(2)}{6 - 2}=\frac{192 - 30}{4}$.

Step3: Calculate the numerator

$192-30 = 162$.

Step4: Calculate the final result

$\frac{162}{4}=40.5$.

Answer:

40.5 bacteria per day