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.)

Answer 1

So since we want to know the rate of change of sales and we have the sales equations as a function of time starting in 1997 ( i.e. t = 0 ), we want to know the rate of change (think derivative) and evaluate this rate of change at t = 1 (this would represent the year 1998)

S(t) = 0.14t² + 0.68t + 3.1    (0 ≤ t ≤ 6). with units of $B

The derivative of sales using the additivity and power rules...

dS/dt = 0.28t + 0.68

so dS/dt evaluated at t = 1 --> 0.28 + 0.68 = 0.96 $B/year or 960 $M/year