Question

A company’s total monthly sales (in millions of dollars) t months from now are given by:

S(t)=0.5t2+3t−5

a) Find S’(t)S’(t) = t + 3

b) Find S(4)S(4) = 15

c) What does the value found in b) represent?This company’s total sales for 4 months is $15 million.

d) Find S’(4)S’(4) = 7

e) What does the value found in d) represent?The sales increase by $7 million a month after the 4 month.

Answer 1

a)
`(dS)/(dt)=S'(t)= 2(0.5) t +3 = t+3`

b)
`S(4) = 0.5*(4^2) +3(4) -5=15 million`

c) For this case we have the total sales $ 15 millions after t =4 months

d)
`S'(4) = 4+3 = 7 million`

e) This value represent the increase in the amount of sales in millions after t=4 months

Step-by-step explanation:

For this case we have the following function for the sales

`S(t) = 0.5 t^2 +3t -5`

Part a

For this case we want to find the derivate of S respect to t and we got:

`(dS)/(dt)=S'(t)= 2(0.5) t +3 = t+3`

Part b

For this case we want to find the value of S when t = 4 so if we replace we got:

`S(4) = 0.5*(4^2) +3(4) -5=15 million`

Part c

For this case we have the total sales $ 15 millions after t =4 months

Part d

For this case we just need to replace t=4 in the derivate and we got:

`S'(4) = 4+3 = 7 million`

Part e

This value represent the increase in the amount of sales in millions after t=4 months