Question

Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.
An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 60 and an x intercept of 18 comma 0.

0 ≤ x ≤ 18, −3.33
0 ≤ x ≤ 18, −0.3
0 ≤ y ≤ 60, −3.33
0 ≤ y ≤ 60, −0.3

Answer 1

Answer:

$0\leq x\leq 30;-3$

Step-by-step explanation:

The graph of exponential function is attached.

The complete question is

Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.

An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 90 and an x intercept of 30 comma 0.

• 0 ≤ y ≤ 90, −0.33
• 0 ≤ y ≤ 90, −3
• 0 ≤ x ≤ 30, −0.33
• 0 ≤ x ≤ 30, −3

The graph shows a decreasing exponential function, which domain is

$0\leq x\leq 30$

Remember that the domain refers to the valid values that the x-variable can use, in this case the graph already shows such values, which are define for $x=0$ to $x=30$.

Now, the average rate of change across the domain refers to the slope of an approximate line which describes the decreasing behaviour. To find such average rate of change we use the initial and final point of the curve, and the following formula

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-90}{30-0}=\frac{-90}{30}=-3$

Therefore the right choice is

$0\leq x\leq 30;-3$

Answer 2

0 < x < 18 , - 3 . 33