Index of environmental quality the department of the

Question

Question: INDEX OF ENVIRONMENTAL QUALITY The Department of the Interior of an African country began to record an index of environmental quality to measure progress or decline in the environmental quality of its wildlife. The index for the years 1998 through 2008 is approximated by the function

I(t) = (50t² + 600)/(t² + 10)            (0 ≤ t ≤ 10)

a. Compute I'(t) and show that I(t) is decreasing on the interval (0, 10).

b. Compute I"(t). Study the concavity of the graph of I.

c. Sketch the graph of I.

d. Interpret your results.