The sales of Universal Instruments in the first t years of its operation are approximated by the function

Question

S(t)= t (squareroot) 0.02t^2+4

where S(t) is measured in millions of dollars. What were Universal's average yearly sales over its first 5 years of operation?

Answer 1

S_Av = 1/5∫₀⁵t√(0.02t² + 4)dt = 1/5·1/0.04(0.02t² + 4)^3/2/(3/2)₀⁵ = 10/3(4.5^3/2 - 4^3/2) ≈ 5.15 mln dollars

Answer 2

S(1) = 1√(0.02 + 4)

S(5) = 5√(0.02⁵ + 4)

S_average = [5√(0.02⁵ + 4) - √0.02 + 4] / 5