Functions and models

Question

Suppose the revenue R from the sale of a product is directly proportional to the number of units x that are sold. Suppose also that the same of 75 units earns a revenue of 1586.25. Find a function for R in terms of x. Answer: R(x)= 

Answer 1

If the revenue (R) is proportional to x, then it has the form:

 

R(x) = kx

 

where k is the constant of proportionality.  To find k, plug in the known point that's given:

 

R(x) = kx

1586.25 = k*75

1586.25/75 = k

 

21.15 = k 

 

k represents the price per unit, $21.15.  The revenue function, then, is:

 

R(x) = ($21.15)x