Question

What is the average rate of change of the function on the interval from x=0 to x=2?

Answer 1

So what I would do is find the slope from (0,f(0)) to (2,f(2))

f(0)=250
f(2)=62.5

(0,250) and (2,62.5)
find the slope
(y2-y1)/(x2-x1)
(62.5-250)/(2-0)=187.5/2=-93.75

answer is -93.75

Answer 2

The average rate of change of the function on the interval from $x = 0$ to $x=2$ is $\boxed{ - 93.75}.$

Further explanation:

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

The formula for average rate of change can be expressed as follows,

$\boxed{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}$

Given:

The function is $f\left( x \right) = 250{\left( {0.5} \right)^x}.$

Explanation:

The given function is $f\left( x \right) = 250{\left( {0.5} \right)^x}$.

Substitute $0$ for $x$ in function $f\left( x \right) = 250{\left( {0.5} \right)^x}.$

$\begin{aligned}f\left( 0 \right) &= 250{\left( {0.5}\right)^0}\\&= 250\times 1\\&= 250\\\end{aligned\\}$

Substitute $2$ for $x$ in function $f\left( x \right) = 250{\left( {0.5} \right)^x}.$

$\begin{aligned}f\left( 2 \right) &= 250{\left( {0.5} \right)^2}\\&= 250 \times 0.25\\&= 62.5\\\end{aligned}$

The average rate of change can be obtained as follows,

$\begin{aligned}A\left( x \right)&=\frac{{f\left( 2 \right) - f\left( 0 \right)}}{{2 - 0}}\\&= \frac{{62.5 - 250}}{2}\\&= \frac{{ - 187.5}}{2}\\&= - 93.75\\\end{aligned}$

The average rate of change of the function on the interval from $x = 0$ to $x=2$ is $\boxed{ - 93.75}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: average rate of change, slope, function, interval, x=2, x=0, $f(x)=250(0.5)^x$, decimal, average rate.