The body mass of a certain type of sheep can be estimated by M(t) = 26.8 + 0.3t - 0.001t^{2}...

Question:

The body mass of a certain type of sheep can be estimated by {eq}\,M(t) = 26.8 + 0.3t - 0.001t^{2}\, {/eq} where {eq}M(t) {/eq} is measured in kilograms and {eq}t {/eq} is days since May 25.

Find the average rate of change of the mass of a sheep between {eq}105 {/eq} and {eq}115 {/eq} days past May 25.

Average Rate of Change of a Function

The average rate of change of the function is used to estimate the average rate at which the function is changing over an interval. The average rate of change of a function {eq}f {/eq} over an interval {eq}\left[a,b\right] {/eq} is defined as: \begin{align*} \Delta f_{avg} = \frac{f(b) - f(a)}{b-a} \end{align*}

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The body mass of the sheep can be estimated by the function {eq}M(t) = 26.8 + 0.3t - 0.001t^{2} {/eq} where {eq}M(t) {/eq} is measured in kilograms...

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Average Rate of Change: Definition, Formula & Examples

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Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.