Studdy AI Logo
Math  /  Data & Statistics

QuestionQuestion Watch Video Show Examples
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 12≤x≤3012 \leq x \leq 30. \begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline 3 & 52 \\ \hline 12 & 40 \\ \hline 21 & 28 \\ \hline 30 & 16 \\ \hline 39 & 4 \\ \hline 48 & -8 \\ \hline \end{tabular}
Answer Attempt 1 out of 2 □\square Submit Answer

Studdy Solution

STEP 1

1. The function is defined by discrete data points given in the table.
2. The average rate of change is calculated using the formula for the slope of the secant line between two points on the graph of the function.

STEP 2

1. Identify the relevant data points for the interval.
2. Apply the formula for the average rate of change.

STEP 3

Identify the data points corresponding to x=12 x = 12 and x=30 x = 30 from the table:
- When x=12 x = 12 , f(x)=40 f(x) = 40 . - When x=30 x = 30 , f(x)=16 f(x) = 16 .

STEP 4

Use the formula for the average rate of change, which is the slope of the secant line between the two points (x1,f(x1))(x_1, f(x_1)) and (x2,f(x2))(x_2, f(x_2)):
Average rate of change=f(x2)−f(x1)x2−x1\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
Substitute the identified values:
x1=12,f(x1)=40,x2=30,f(x2)=16x_1 = 12, \quad f(x_1) = 40, \quad x_2 = 30, \quad f(x_2) = 16
Average rate of change=16−4030−12\text{Average rate of change} = \frac{16 - 40}{30 - 12}

STEP 5

Calculate the differences:
16−40=−2416 - 40 = -24 30−12=1830 - 12 = 18

STEP 6

Divide the differences to find the average rate of change:
−2418=−43\frac{-24}{18} = -\frac{4}{3}
The average rate of change of the function over the interval 12≤x≤3012 \leq x \leq 30 is:
−43\boxed{-\frac{4}{3}}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord