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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

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 funct class=

Respuesta :

Poltergeist

Answer:

0 ≤ x ≤ 30, −3 is the answer.

Step-by-step explanation:

The domain of the function is all the x values between the highest and the lowest values of x.

The graph shows that the function starts at [tex]x=0[/tex] and ends at [tex]x=30[/tex]; and it is not defined for [tex]x>30[/tex] and [tex]x<0[/tex]; therefore the domain is

[tex]\boxed{0\leq x\leq 30.}[/tex]

The average rate of change of the function is the slope of the line that best approximates the function, and we see that a line from [tex](0,90)[/tex] to [tex](30,0)[/tex] best approximates the function, and its slope is:

[tex]\frac{90-0}{0-30} =-3[/tex]

Therefore the average slope is -3.

So the correct choice is the third one: [tex]0\leq x\leq 30, -3[/tex]

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