What is the average rate of change of the function on the interval from x = 0 to x = 5? f(x)=1/2(3)x

3 answers
Question:

What is the average rate of change of the function on the interval from x = 0 to x = 5?
f(x)=1/2(3)x
enter your answer, as a decimal, in the box.

Answers

from 0 to 7.5

Step-by-step explanation:

Just plug in (x)

f(5)=1/2(3)5

1 and 1/2*5

>>7.5<<

[tex]m = 24.2[/tex]

Step-by-step explanation:

The value of each extreme is presented below:

[tex]f(0) = \frac{1}{2}\cdot 3^{0}[/tex]

[tex]f(0) = 0.5[/tex]

[tex]f(5) = \frac{1}{2}\cdot 3^{5}[/tex]

[tex]f(5) = 121.5[/tex]

The average rate of change of the function is:

[tex]m = \frac{121.5 - 0.5}{5-0}[/tex]

[tex]m = 24.2[/tex]

What is the average rate of change of the function on the interval from x = 0 to x = 5 ; f(x)= 1\2 (3)^x

Average rate of change of the function on the interval from x = 0 to x = 5 is 24.2

Solution:

Given function is:

[tex]f(x) = \frac{1}{2}(3^x)[/tex]

We have to find the average rate of change of function from x = 0 to x = 5

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

[tex]{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}[/tex]

So for rate of change of function from x = 0 to x = 5 is:

[tex]{A\left( x \right) = \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}}[/tex]

Let us find f(0) and f(5)

To find f(0), substitute x = 0 in f(x)

[tex]f(0) = \frac{1}{2}(3^0) = \frac{1}{2}[/tex]

To find f(5), substitute x = 5 in f(x)

[tex]f(5) = \frac{1}{2}(3^5) = \frac{1}{2}(243) = \frac{243}{2}[/tex]

Therefore,

[tex]A(x)=\frac{\frac{243}{2}-\frac{1}{2}}{5-0}=\frac{242}{\frac{2}{5}}=\frac{242}{2} \times \frac{1}{5}=24.2[/tex]

Therefore average rate of change of the function on the interval from x = 0 to x = 5 is 24.2

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