Question

Use the graph representing bacteria decay two estimate the domain of the function and sulfur the average rate of change across the domain.

Answer 1

Answer: Choice C

$\text{Domain}: 0 \le x \le 55$ and $\text{Average rate of change over domain} = -1.45$ (average rate of change is approximate)

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The domain is the set of allowed x inputs of the function. The smallest x value shown is x = 0, which is from the point (0,80). The largest x value possible is x = 55 from the point (55,0)

The domain is the set of all values between 0 and 55, including both endpoints. Therefore, we get a domain of $0 \le x \le 55$

Compute the slope of the line through (0,80) and (55,0) to find the average rate of change over the entire function domain.

m = (y2 - y1)/(x2 - x1)

m = (0 - 80)/(55 - 0)

m = -80/55

m = -1.45 approximately

The slope of the line through (0,80) and (55,0) is approximately -1.45, which is also the average rate of change over the entire domain.

Side note: the negative slope or negative rate of change indicates we are going downhill ultimately as we move from left to right.