Question

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) = 0.882A0.842
where A is measured in square meters.† Find S'(103). (Round your answer to five decimal places.)
S'(103) =
species/m2

Answer 1

The rate of change of species with respect to area at 103 square meters in the Pasoh Forest Reserve in Malaysia is approximately 0.36476 species/m2, after calculating the derivative of the power function S(A) using the power rule and evaluating at A = 103.

Step-by-step explanation:

To find S'(103), which is the derivative of S with respect to A evaluated at A = 103 m2, we will use the power rule for differentiation.

The power function given is S(A) = 0.882A0.842.

Applying the power rule, the derivative S'(A) is equal to 0.842 × 0.882A0.842-1.

Now, we substitute A with 103 to get S'(103):

S'(103) = 0.842 × 0.882 × 1030.842-1
= 0.742764 × 103-0.158

Calculating to obtain the decimal value for 103-0.158 and then multiplying it by 0.742764 gives us the approximate value of:

S'(103) = 0.36476

Therefore, the rate of change of species with respect to area at 103 m2 is approximately 0.36476 species/m2, rounded to five decimal places.