Question

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

Answer 1

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 2

Option C -
`h(x)=2(5(1.2)^x+6x)` x = 4 months

Explanation:

Given : 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`.

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

`h(x)=f(x)+g(x)`

`h(x)=12x+10(1.2)^x`

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

But we have given in thousands dollars,

∴
`(68736)/(1000)=68.736`

`12x+10(1.2)^x=68.736`

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:

`h(x)=12x+10(1.2)^x=2(5(1.2)^x+6x)`

Therefore, Option C is correct
`h(x)=2(5(1.2)^x+6x)`

x = 4 months