Question

1. Thefunction,?=?(?),representstheamountofsolidwastegeneratedbyUScities,inmillionsof tons, as a function of time, ?, in years since 1995. Given ?(2) = 227.78 and ?′(2) = 5.24, which choice is an interpretation for the relative rate of change ? at ? = 2.

   (A) In 1997, the amount of solid waste generated by US cities was decreasing by about 2% per year.
   (B) In 1997, the amount of solid waste generated by US cities was decreasing by about 2.3% per year.

   (C) In 1997, the amount of solid waste generated by US cities was increasing by about 2% per month.
   (D) In 1997, the amount of solid waste generated by US cities was increasing by about 2.3% per year.

Answer 1

Derivative of any function gives the rate of change of that function

Here at t=2 i.e in 1997 f'(2)=5.24

f'(2) is positive this indicate the function is increasing

Percentage increase=

Therefore option(D) is correct answer

(D)in 1997 the amount of solid waste generated by US cities was increasing by about 2.3% per year

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