the revenue that an apparel company earns each month for its different product lines fluctuates throughout…

the revenue that an apparel company earns each month for its different product lines fluctuates throughout the year. over the course of a year, the revenue earned from clothing sales each month is modeled by function c, where x is the number of months since the beginning of the year. the revenue earned from sales of shoes and accessories each month is modeled by function s, where x is the number of months since the beginning of the year. $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$ use this information to complete the statement. between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is at the revenue earned from sales of clothing.

the revenue that an apparel company earns each month for its different product lines fluctuates throughout the year. over the course of a year, the revenue earned from clothing sales each month is modeled by function c, where x is the number of months since the beginning of the year. the revenue earned from sales of shoes and accessories each month is modeled by function s, where x is the number of months since the beginning of the year. $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$ use this information to complete the statement. between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is at the revenue earned from sales of clothing.

Answer

Explanation:

Step1: Calculate revenue of shoes/accessories at x = 3

Substitute x = 3 into $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$. [ \begin{align*} s(3)&=0.6\times3^{3}-10.2\times3^{2}+32.4\times3 + 127.2\ &=0.6\times27-10.2\times9 + 97.2+127.2\ &=16.2-91.8+97.2 + 127.2\ &=(16.2+97.2+127.2)-91.8\ &=240.6 - 91.8\ &=148.8 \end{align*} ]

Step2: Calculate revenue of shoes/accessories at x = 6

Substitute x = 6 into $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$. [ \begin{align*} s(6)&=0.6\times6^{3}-10.2\times6^{2}+32.4\times6+127.2\ &=0.6\times216-10.2\times36 + 194.4+127.2\ &=129.6-367.2+194.4 + 127.2\ &=(129.6+194.4+127.2)-367.2\ &=451.2-367.2\ &=84 \end{align*} ]

Step3: Calculate rate of change of shoes/accessories revenue

The rate of change formula is $\frac{s(6)-s(3)}{6 - 3}=\frac{84 - 148.8}{3}=\frac{- 64.8}{3}=-21.6$.

Step4: Estimate clothing - revenue rate of change from graph

At x = 3, estimate $c(3)\approx130$, at x = 6, estimate $c(6)\approx70$. The rate of change is $\frac{c(6)-c(3)}{6 - 3}=\frac{70 - 130}{3}=\frac{-60}{3}=-20$.

Answer:

a slower rate than