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.

Answer 1

• 0 ≤ x ≤ 18
• -3.33

Further explanation

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.

Learn more

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

Answer 2

The domain of a function is the set of input values of the function.

• The domain of the function is: [0,18]
• The average rate of change across the domain is -3.33

From the graph, we have the following highlights.

• The graph starts from the origin
• The graph ends at x = 18

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

The average rate of change is calculated as:

$\mathbf{m = \frac{f(b) - f(a)}{b - a}}$

From the graph, we have:

$\mathbf{f(0) = 60}$

$\mathbf{f(18) = 0}$

So, we have:

$\mathbf{m = \frac{f(18) - f(0)}{18 - 0}}$

This gives

$\mathbf{m = \frac{0 - 60}{18}}$

$\mathbf{m = -\frac{ 60}{18}}$

$\mathbf{m = -3.33}$

Hence, the average rate of change across the domain is -3.33

Read more about exponential functions at:

https://brainly.com/question/18719551