How fast (in billions of dollars per year) were sales increasing at the beginning of 1998?

Question

The annual sales of digital signal processors (DSPs) in billions of dollars is approximated by

S(t) = 0.14t² + 0.68t + 3.1    (0 ≤ t ≤ 6)

where t is measured in years, with t = 0

 corresponding to the beginning of 1997.† (Round your answers to two decimal places.)

(a)

What were the sales (in billions of dollars) of DSPs at the beginning of 1997?

$  3.10 billion

(b)

How fast (in billions of dollars per year) was the level of sales increasing at the beginning of 1997?

$ 0.68 billion/year

Answer 1

a) S(0) = 0.14·0² +0.68·0 + 3.1 = $3.10 billion

b) S'(t) = 0.28t + 0.68; S'(0) = 0.28·0 + 0.68 = $0.68 billion/year