contestada

The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50

$0.67

$1.07

$1.50

Book sold Profit f(x)
(X)
100       ║   $50.00
250      ║      $275.00
300      ║      $350.00
350     ║     $425.00

answer is A-$0.50

Respuesta :

frika

You are given a table

[tex]\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \$50\\250 & \$275\\300 & \$350\\350 & \$450\end{array}[/tex]

The rate of change for the function represented in the table can be calculated using the formula

[tex]\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},[/tex]

where i=1,2,3.

1. When i=1,

[tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5[/tex]

2. When i=2,

[tex]\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5[/tex]

3. When i=3,

[tex]\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5[/tex]

Then the rate of change is $1.5

Answer: correct choice is D.

The rate of change for the function is [tex]\$ 1.5[/tex]

The rate  of change for the function is calculate by the formula

[tex]\frac{y_{n+1}-y_n}{x_{n+1}-x_n}[/tex]

Where [tex]n=1,2,3[/tex].

A) when [tex]n=1[/tex]

[tex]\frac{y_{1+1}-y_1}{x_{1+1}-x_1}=\frac{y_{2}-y_2}{x_{2}-x_2}[/tex]

[tex]\dfrac{275-50}{250-100}=\dfrac{225}{100}[/tex]

Hence Rate of change when [tex]n=1[/tex] is [tex]1.5[/tex]

B)when [tex]n=2[/tex]

[tex]\frac{y_{2+1}-y_2}{x_{2+1}-x_2}=\frac{y_{3}-y_2}{x_{3}-x_2}[/tex]

[tex]\dfrac{350-275}{300-250}=\dfrac{75}{50}[/tex]

Hence Rate of change when [tex]n=2[/tex] is [tex]1.5[/tex]

C) when [tex]n=3[/tex]

[tex]\frac{y_{3+1}-y_3}{x_{3+1}-x_3}=\frac{y_{4}-y_3}{x_{4}-x_3}[/tex]

[tex]\dfrac{425-350}{350-300}=\dfrac{75}{50}[/tex]

Hence Rate of change when [tex]n=3[/tex] is [tex]1.5[/tex]

So the rate of change for function represented in the table is same for different value of [tex]n[/tex] i.e, [tex]\$ 1.5[/tex].

Learn more about function here;

https://brainly.com/question/12934295?referrer=searchResults

Ver imagen shubheetutor

Otras preguntas