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.

Answer 1

Answer:

Option C - $h(x)=2(5(1.2)^x+6x)$  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 $f(x) = 12x$ .

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,

∴ $\frac{68736}{1000}=68.736$

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

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

Answer 2

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