Question

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by , where is the number of hours since 10 AM, .

Answer 1

Complete 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) = -4t^2 + 20t + 60`, where is the number of hours since 10 AM:

a) Find an expression for the revenue per hour as a function of x, R(x)

b) Find and simplify, R(x(t))

Answer:

a) R(x) = 2x

b)
`R(x(t)) = -8t^2 + 40t + 120`

Explanation:

a) This is a very trivial exercise.

`x(t) = -4t^2 + 20t + 60`

The number of hot dogs sold per hour is given by x

Charge per hot dog = $2

An expression of revenue per hour,R, as a function of the number of hot dogs sold per hour, x, is therefore: R(x) = 2x

b)
`x(t) = -4t^2 + 20t + 60`

R(x(t)) = 2(x(t))

`R(x(t)) = 2(-4t^2 + 20t + 60)\\R(x(t)) = -8t^2 + 40t + 120`