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.
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.