Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by
x(t) = −4t2 + 20t + 80,
where t is the number of hours since 10 AM,
0 ≤ t ≤ 4.
Find an expressio for the revenue per hour in terms of x. R(x)=?

Question

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by 
x(t) = −4t2 + 20t + 80,
 where t is the number of hours since 10 AM, 
0 ≤ t ≤ 4.
 Find an expressio for the revenue per hour in terms of x. R(x)=?

anonymous · Answer

$$

R(2) = 2 x(t)= 2( -4 t^2 + 20 t +80)= -8t^2 -80 t+ 320

$$
Where t is the number of hour since 10 am

jim_thompson5910 · Answer

If x is the number of hot dogs, and you want a function in terms of x, then

R(x) = 2x

jim_thompson5910 · Answer

Basically, you earn 2x dollars for selling x hot dogs.

anonymous · Answer

Thanks guys!

anonymous · Answer

$$
R(t) = 2 x(t)= 2( -4 t^2 + 20 t +80)= -8t^2 -80 t+ 320
$$

anonymous · Answer

Right but that gives revenue per hour as a function of time. not revenue per hour.

anonymous · Answer

it was simple but I had a brain fart.