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 https://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.
