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# The number of tree species $S$ in a given area $A$ in the Pasoh Forest Reserve in Malaysia has been modeled by the power function $S(A) = 0.882A^0.842$where A is measured in square meters. Find $S' (100)$ and interpret your answer.

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Hey, it's Claire. So when you read here, you have us of A is equal to 0.882 A. To the point 84 to power. We're going to differentiate it. Using the power of all we got a 0.743 A. It is a negative 0.158 power. We substitute 100 for a We get around 0.36 maybe around two decimals. And that means there are 100 tree species in 0.36 square meters.

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