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Math  /  Data & Statistics

QuestionGiven the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 25≤x≤8525 \leq x \leq 85. \begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline 10 & 52 \\ \hline 25 & 43 \\ \hline 40 & 34 \\ \hline 55 & 25 \\ \hline 70 & 16 \\ \hline 85 & 7 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function is defined by discrete points given in the table.
2. The average rate of change of a function f(x) f(x) over an interval [a,b][a, b] is given by the formula f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}.

STEP 2

1. Identify the values of f(x) f(x) at the endpoints of the interval.
2. Apply the formula for the average rate of change.

STEP 3

Identify the values of f(x) f(x) at x=25 x = 25 and x=85 x = 85 from the table:
f(25)=43 f(25) = 43 f(85)=7 f(85) = 7

STEP 4

Apply the formula for the average rate of change:
Average rate of change=f(85)−f(25)85−25\text{Average rate of change} = \frac{f(85) - f(25)}{85 - 25}
Substitute the known values:
=7−4385−25= \frac{7 - 43}{85 - 25}

STEP 5

Simplify the expression:
=−3660= \frac{-36}{60}
Reduce the fraction to simplest form:
=−35= \frac{-3}{5}
The average rate of change of the function over the interval 25≤x≤85 25 \leq x \leq 85 is:
−35 \boxed{-\frac{3}{5}}

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