The average rate of change of the function on the interval from [tex]x = 0[/tex] to [tex]x=5[/tex] is [tex]\boxed{\frac{{2904}}{5}}.[/tex]
Further explanation:
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
The formula for average rate of change can be expressed as follows,
[tex]\boxed{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}[/tex]
Given:
The function is [tex]f\left( x \right) = 12{\left( {3} \right)^x}.[/tex]
Explanation:
The given function is [tex]f\left( x \right) = 12{\left( {3} \right)^x}.[/tex]
Substitute [tex]0[/tex] for [tex]x[/tex] in function [tex]f\left( x \right) = 12{\left( {3} \right)^x}.[/tex]
[tex]\begin{aligned}f\left(0\right) &= 12{\left( 3 \right)^0}\\&= 12 \times 1\\&= 12\\\end{aligned}[/tex]
Substitute 5 for [tex]x[/tex] in function [tex]f\left( x \right) = 12{\left( {3} \right)^x}.[/tex]
[tex]\begin{aligned}f\left( 5 \right) &= 12{\left( 3 \right)^5}\\&= 12 \times \left( {243} \right)\\&= 2916\\\end{aligned}[/tex]
The average rate of change can be obtained as follows,
[tex]\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}[/tex]
The average rate of change of the function on the interval from [tex]x = 0[/tex] to [tex]x=5[/tex] is [tex]\boxed{\frac{{2904}}{5}}.[/tex]
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, [tex]x=2, x=0, f(x)=12(3)^x,[/tex] decimal, average rate.
