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madreJ [45]
3 years ago
5

What is the average rate of change of the function f(x)=2(3)x from x = 2 to x = 4?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
6 0

The average rate of change of function is 72.

<u>SOLUTION: </u>

Given that, we have to find the average rate of change of the function f(x)=2(3)x from x = 2 to x = 4  

Use the slope formula to find the average rate of change:  

\begin{array}{l}{m=\frac{y 2-y 1}{x 2-x 1}} \\\\ {m=\frac{f(4)-f(2)}{4-2}} \\\\ {m=\frac{f(4)-f(2)}{2}}\end{array}

To simplify this, we need to find values of f ( 4 ) and f ( 2 ) :  

\begin{array}{l}{f(4)=2 x(3)^{4}=2(81)=162} \\\\ {f(2)=2(3)^{2}=2(9)=18} \\\\ {m=\frac{162-18}{2}} \\\\ {m=\frac{144}{2}} \\\\ {m=72}\end{array}

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Answer:

1.) m^{15}

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Give me a comment if you want the explanation.

1.) \mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0

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\mathrm{Multiply\:the\:numbers:}\:3\cdot \:5=15

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2.) \mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0

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3 years ago
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