The profit, in thousands of dollars, from the DVD sales of a TV show over x months is given by the function f(x) = 12x.

The profit, in thousands of dollars, from online streaming of the same TV show over x months is given by the function g(x) = 10(1.2)x.

Which function best describes the total profit from the TV show over x months, and after how many months will the profit be approximately $68,736?

A)h(x) = 22x(1.2)x
x = 2 months

B)h(x) = 2(6(1.2)x + 5x)
x = 4 months

C)h(x) = 2(5(1.2)x + 6x)
x = 4 months

D)h(x) = 2(5(1.2)x - 6x)
x = 18 months

all you need to do is find (f+g)x = (12x) + (10(1.2)X) which = 24x
then in the multiple choice, see which one equals 24x, in this case its C.
5*1.2=6, 6x+6x = 12x*2 = 24x

Answer Link

tardymanchester tardymanchester · Answer 2 · 2019-01-21T06:59:53+01:00

Answer:

Option C - [tex]h(x)=2(5(1.2)^x+6x)[/tex] x = 4 months

Step-by-step explanation:

Given : The profit, in thousands of dollars, from the DVD sales of a TV show over x months is given by the function [tex]f(x) = 12x[/tex] .

The profit, in thousands of dollars, from online streaming of the same TV show over x months is given by the function [tex]g(x) = 10(1.2)^x[/tex].

To find : Which function best describes the total profit from the TV show over x months, and after how many months will the profit be approximately $68,736

Solution : Firstly, Total profit from the TV shows over x months is

[tex]h(x)=f(x)+g(x)[/tex]

[tex]h(x)=12x+10(1.2)^x[/tex]

To find the value of x put the profit given $68,736

But we have given in thousands dollars,

∴ [tex]\frac{68736}{1000}=68.736[/tex]

[tex]12x+10(1.2)^x=68.736[/tex]

We solve this equation through graph, (graph attached)

At y=68.736 the value of x=4

∴ x = 4 months

We can also re-write the function in the form:

[tex]h(x)=12x+10(1.2)^x=2(5(1.2)^x+6x)[/tex]

Therefore, Option C is correct [tex]h(x)=2(5(1.2)^x+6x)[/tex]

x = 4 months