Mathematics, 27.10.2019 22:43, kayladgranger

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

Use the graph representing bacteria decay to estimate the domain of the function and solve for the a

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answered: RonGeffrard9597

0 ≤ x ≤ 18-3.33Further 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 moreWhat are the domain and range of the function f(x) = 3x + 5? linkWhat is the range of the given function? {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)} linkThe piecewise-defined functions link

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

answered: Guest

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

answered: Guest