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Serhud [2]
3 years ago
6

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

the domain.

Mathematics
2 answers:
nasty-shy [4]3 years ago
5 0

Answer:

Domain is [0,18]

Average rate of change of bacteria per minute is -3333.33.

Step-by-step explanation:

Domain is the possible values of x.

From the graph, it's clear that the x values ranges from 0 to 18 as the end points of the graph are (0,60) and (18,0)

So, domain of the function is [0,18].

Now, average rate of change is negative as there is bacteria decay.

Average rate of change is given as the negative ratio of y intercept to the x intercept.

Here, x-intercept is 18 and y-intercept is 60000.

So, average rate of change is given as,

R_{avg}=-\frac{60000}{18}=-3333.33

Therefore, average rate of change of bacteria per minute is -3333.33.

ollegr [7]3 years ago
3 0
  • 0 ≤ x ≤ 18
  • -3.33
<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 \ }

The formula for the average rate of change on a given interval [a, b] is as follows:

\boxed{ \ \frac{\Delta y}{\Delta x} = \frac{f(b) - f(a)}{b - a} \ }

Because the domain of the function is [0, 18], we prepare:

  • \boxed{(0, 60) \ as \ (a, f(a))} and
  • \boxed{(18, 0) \ as \ (b, f(b))}

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} \ }

\boxed{ \ \frac{\Delta y}{\Delta x} = \frac{- 60}{18} \ }

\boxed{\boxed{ \ \frac{\Delta y}{\Delta x} = -3.33 \ }}

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>
  1. What are the domain and range of the function f(x) = 3x + 5? brainly.com/question/3412497
  2. What is the range of the given function? {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)} brainly.com/question/1435353
  3. 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

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