Mathematics: Find the average rate of change f(x)=x^2−6x+8 when x2=1 and x1=3

Find the average rate of change f(x)=x^2−6x+8 when

jcbballer

17.03.2022

Average rate of change for given function is: -2

Step-by-step explanation:

Given function is:

$f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3$

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

$f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3$

The formula for finding the rate of change is:

$Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}$

Putting the values, we get

$=\frac{3-(-1)}{1-3}\\=\frac{3+1}{-2}\\=\frac{4}{-2}\\= -2$

Hence,

Average rate of change for given function is: -2

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dg12300

24.02.2023

2000 customers paid the old rate and 500 customers paid the new rate.

Step-by-step explanation:

The new renewal rate is twice the old rate. That is $250\times2=500$ dollars

Let x be the old rate.

Let y be the new rate.

As given: Your income from renewals was $750,000 this year.

So, we have the following equation:

250x +500y =750000 or x+2y= 3000 .....(1)

And total you have 2500 customers, so we get the following equation:

x+y= 2500 .....(2)

Deriving x=2500-y from (2) and substituting in (1)

2500-y+2y= 3000

=> y=3000-2500

y = 500

x=2500-500

x = 2000

Hence, 2000 customers paid the old rate and 500 customers paid the new rate.

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