Question

The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars. 2010 dollars (RP)(t) dollars (at pump) dollars Rit dollars gallon + P(t) gallon gallon gallon O R(t) dollars - P(t) 2010 dolars(R P)(t) 2010 dollars gallon dollars (at pump) dollars (at pump) R(t) gallon · dollars (at pump) R(t)--+ P() dollars (at pump) A(t) dollars . Pit), 2010 dollars 2010 dollars 2010 dollars _- (R- P)(t) dollars gallon 2010 dollars dollars 2010 dollars _- (R + P)(t) gallon (b) What are the output units of the new function? 2010 dollars per gallon gallons per 2010 dollar dollars per gallon 2010 dollars per dollar (at pump) gallons per dollar

Answer 1

a) F(t) = R[P(t)]

b) the output units of the new function = F(t) in dollars per gallon

Explanation:

a) There are two function R(t) which shows the average price in dollars of a gallon of regular unleaded gasoline and P(t) which shows the purchasing power of the dollar as measured by consumer prices based on 2010 dollars.

To write the function which gives the rice of gasoline in constant 2010 dollars ;

From the analysis , this is an example of a composition of function as such the relationship =

F(t) = R[P(t)]

b) the output units of the new function = F(t) in dollars per gallon

This shows that the value of F(t) is the dependent variable