Give the rate of change of sales revenue of a store modeled by the equation $S'(t)= -30t^{2} + 420t$ . The Total sales revenue function S(t) can be gotten by integrating the function given as shown;

$\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\ S(t)= -10t^{3} +210t^{2} \\$

a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;

$Given\ S(t) = -10t^{3} + 210t^{2}$

$S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860$

Total sales = S(7) - S(0)

= 6,860 - 0

Total sales for the first week = $6,860

b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;

Total sales for the second week = S(14)-S(7)

Given S(7) = 6,860

To get S(14);

$S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720$

The total sales for the second week after campaign ends = 13,720 - 6,860

= $6,860

8 0

3 years ago

What is the domain of the function represented by the graph

Dimas [21]

Answer:

Step-by-step explanation:

Domain of the function is the whole R

5 0

2 years ago

I’ll mark you brainlist I’ll mark you brainlist

Margaret [11]

Answer:

answer is 0

Step-by-step explanation:

5 0

3 years ago