<h3>
Further explanation</h3>
The domain of a function is the set of values of the independent variable for which a function is defined. The domain is located along the x-axis where the graph is defined from the starting point to the endpoint.
From the graph, we can see that:
- the horizontal axis is the amount of time (in minutes)
- the vertical axis is the number of bacteria (in thousands)
- (0, 60) is a y-intercept
- (18, 0) is an x-intercept
Also from the graph, we can observe that the values of x start from x = 0 to x = 18.
Thus the domain of the function is ![\boxed{ \ [0, 18] \ or \ 0 \leq x \leq 18 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%5B0%2C%2018%5D%20%5C%20or%20%5C%200%20%5Cleq%20x%20%5Cleq%2018%20%5C%20%7D)
The formula for the average rate of change on a given interval
is as follows:
![\boxed{ \ \frac{\Delta y}{\Delta x} = \frac{f(b) - f(a)}{b - a} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D%20%5C%20%7D)
Because the domain of the function is [0, 18], we prepare:
and![\boxed{(18, 0) \ as \ (b, f(b))}](https://tex.z-dn.net/?f=%5Cboxed%7B%2818%2C%200%29%20%5C%20as%20%5C%20%28b%2C%20f%28b%29%29%7D)
And now, let us solve for the average rate of change across the domain.
![\boxed{ \ \frac{\Delta y}{\Delta x} = \frac{0 - 60}{18 - 0} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cfrac%7B0%20-%2060%7D%7B18%20-%200%7D%20%5C%20%7D)
![\boxed{ \ \frac{\Delta y}{\Delta x} = \frac{- 60}{18} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cfrac%7B-%2060%7D%7B18%7D%20%5C%20%7D)
![\boxed{\boxed{ \ \frac{\Delta y}{\Delta x} = -3.33 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20-3.33%20%5C%20%7D%7D)
Note that the y-values change down 3.33 units in thousands every time the x-values change 1 unit in minutes, at intervals of the domain.
We conclude that from t = 0 to t = 18 (in minutes), every 1 minute as many as 3.33 thousand bacteria decay.
<h3>Learn more</h3>
- What are the domain and range of the function f(x) = 3x + 5? brainly.com/question/3412497
- What is the range of the given function? {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)} brainly.com/question/1435353
- The piecewise-defined functions brainly.com/question/9590016
Keywords: use, the graph, representing, bacteria decay, to estimate, the domain of the function, and, solve, the average rate of change, axis, horizontal, vertical, intervals, minutes, thousand, 0, 18, 60, -3.33