The function Pt gives gas prices in units of dollars per gal

The function P(t) gives gas prices (in units of dollars per gallon) as a function of t the year (in A.D. or C.E.), and g(t) is the gas consumption rate measured in gallons per year by a driver as a function of their age. The function g is certainly dierent for dierent people. Assuming a lifetime is 100 years, what function gives the total amount spent on gas during the lifetime of an individual born in an arbitrary year t? Is the operator that maps g to this function linear?

Solution

P(t) gives gas price . means

Time changes p(t) also changes.

G(t) gives gas consumption at years.

So total price of gas at certain year= p(t)*g(t)

G(t) is a linear function because it give straight line.

That is time increases gas consumption also increase and vice versa