The average rate of change of the function on the interval from \(x = 0\) to \(x=5\) is \(\boxed{\frac{{2904}}{5}}.\)
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 \(f\left( x \right) = 12{\left( {3} \right)^x}.\)
Explanation:
The given function is \(f\left( x \right) = 12{\left( {3} \right)^x}.\)
Substitute \(0\) for \(x\) in function \(f\left( x \right) = 12{\left( {3} \right)^x}.\)
\(\begin{aligned}f\left(0\right) &= 12{\left( 3 \right)^0}\\&= 12 \times 1\\&= 12\\\end{aligned}\)
Substitute 5 for \(x\) in function \(f\left( x \right) = 12{\left( {3} \right)^x}.\)
\(\begin{aligned}f\left( 5 \right) &= 12{\left( 3 \right)^5}\\&= 12 \times \left( {243} \right)\\&= 2916\\\end{aligned}\)
The average rate of change can be obtained as follows,
\(\begin{aligned}A\left( x \right)&= \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}\\&= \frac{{2916 - 12}}{5}\\&=\frac{{2904}}{5}\\\end{aligned}\)
The average rate of change of the function on the interval from \(x = 0\) to \(x=5\) is \(\boxed{\frac{{2904}}{5}}.\)
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, \(x=2, x=0, f(x)=12(3)^x,\) decimal, average rate.
