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Let f(x)=ln(3x)+2.5 .



What is the average rate of change of f(x) from 2 to 7?

Round your answer to the nearest hundredth.

Respuesta :

carlosego
For this case what we should do is evaluate the function in each of the points from 2 to 7 and then find the average.
 We have then:
 f (x) = ln (3x) +2.5.
 f (2) = ln (3 * 2) + 2.5 = 4.291759469
 f (3) = ln (3 * 3) + 2.5 = 4.697224577
 f (4) = ln (3 * 4) + 2.5 = 4.98490665
 f (5) = ln (3 * 5) + 2.5 = 5.208050201
 f (6) = ln (3 * 6) + 2.5 = 5.390371758
 f (7) = ln (3 * 7) + 2.5 = 5.544522438
 Then the average is:
 Average = (4.291759469 + 4.697224577 + 4.98490665 + 5.208050201 + 5.390371758 + 5.544522438) / (6) = 5.019472516
 nearest hundredth
 5.02
 Answer:
 the average rate of change of f (x) from 2 to 7 is  5.02

aksnkj

The average rate of change of [tex]f(x)[/tex] is [tex]4.73[/tex].

Given,

[tex]f(x)=ln(3x)+2.5[/tex].

We have to calculate the average rate of change, from [tex]x[/tex] varies [tex]2 [/tex] to [tex]7[/tex].

So, we calculate the value of [tex]f(x)[/tex] at [tex]x=2, 3 ,4 ,5,6,7[/tex] and calculate the average.

How to calculate the average rate?

Here at [tex]x=2[/tex],

[tex]f(2)=ln(3 \times 2)+2.5=ln(6)+2.5[/tex]

So,

[tex]f(2)=1.79+2.5=4.291[/tex].

Similarly,

[tex]f(3)=ln(3 \times 3)+2.5=ln(9)+2.5[/tex]

[tex]f(3)=2.197+2.5=4.697[/tex]

Again,

[tex]f(4)=ln(3 \times 4)+2.5=ln(12)+2.5[/tex]

[tex]f(4)=2.484+2.5=4.984[/tex]

Again,

[tex]f(5)=ln(3 \times 5)+2.5=ln(15)+2.5\\[/tex][tex]f(5)=5.208[/tex]

Again,

[tex]f(6)=ln(3 \times 6)+2.5=ln(18)+2.5\\[/tex][tex]f(6)=5.390[/tex]

Again,

[tex]f(7)=ln(3 \times 7)+2.5=ln(21)+2.5[/tex]

[tex]f(7)=3.822[/tex]

Now Average Rate of change of [tex]f(x)[/tex] from 2 to 7 will be,

[tex]\frac{f(2)+f(3)+f(4)+f(5)+f(6)+f(7)}{6}=\frac{4.291+4.697+4.984+5.208+5.390+3.822}{6}[/tex]

[tex]=4.732[/tex].

On rounding it off to the nearest hundredth the average rate of change of[tex]f(x)[/tex] is [tex]4.73[/tex].

Hence the average rate of change of [tex]f(x)[/tex] is [tex]4.73[/tex].

For more details on Average follow the link below:

https://brainly.com/question/897199

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