Answer:
S'(t) = 0.09t^2 + t + 9
S(2) = 24.24
S'(2) = 11.36
S(11) = 203.43 means that the sales of the company 11 months from now is $203,430,000.
S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month
Step-by-step explanation:
The derivate of the sales function S'(t) , which is the rate at which sales vary with time in months, is:
[tex]\frac{dS(t)}{dt} =S'(t) = 0.09t^2 + t + 9[/tex]
S(2) is found by applying t=2 to S(t):
[tex]S(2) = 0.03*(2^3) + 0.5*(2^2) + 9*2 + 4\\S(2)= 24.24[/tex]
S'(2) is found by applying t=2 to S'(t):
[tex]S'(2) = 0.09*(2^2) + 2 + 9\\S'(2) = 11.36[/tex]
Since the sales function gives the amount of sales in millions of dollars,
S(11) = 203.43 means that the sales of the company 11 months from now is $203,430,000.
S'(t) represents the rate of change in sales in millions of dollars per month.
S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month
