Answer to Question #239927 in Calculus for Silky

Question

Question 4

A vehicle has a 20-gal tank and gets 15mpg. The number of miles N that can be driven depends on the amount of gas 𝑥 in the tank:

a) Write a formula that models this situation.

b) Determine the number of miles the vehicle can travel on (i) a full tank of gas, and (ii)

3/4 of a tank of gas.

c) Determine the domain and range of the function.

d) Determine how many times the driver had to stop for gas if she has driven a total of

578 mile

Answer 1

a) The model that describes this situation will be

$N{(x)}=(20\,gal)(15\frac{miles}{gal})x=[300\,miles]x$

b) we proceed to calculate the mileage by substituting x=1 and x=3/4 for the tank level:

$N(x=1)=[300\,miles](1)=300\,miles \\ N(x=3/4)=[300\,miles](3/4)=225\,miles$

c) The domain of N(x) would be $0\leq x \leq 1$ and the range will be $0\,miles\leq N(x) \leq 300\,miles$

d) We have to calculate x:

$N'=578\,miles=[300\,miles]x' \\ \implies x'=578\,miles/300\,miles=1.926$

In conclusion, the driver has to stop only once during the whole trip to fill the tank.