Question

Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you?

Answer 1

Answer:

See explanation below.

Explanation:

Let's define some notattion first:

C represent the total cost for the trip on $ dollars

p represent the price of gasolin per gallon

d would represent the distance on miles

t would represent the mileage per gallon

For this case we can calculate the total cost for the trip with the following formula:

$C =\frac{2 dp}{t}$

The 2 is because we are assuming that we travel the distance and then we go back the same distance,

We can check the units and we have:

$\frac{mi *dollars/gal}{\frac{mi}{gal}} = dollars$

What assumptions or approximations are necessary to treat this model as a deterministic model?

If we want a deterministic model then we cant' have any stoschastical component on this model or something with a random variable. And we need to satisfy some conditions:

a) The distance needs to be a constant and known

b) The price needs to be constant for all the trip

c) The mileage needs to be constant and known

Are these assumptions or approximations acceptable to you?

If we analyze the assumptions we see that all the conditions are difficult to satisfy since in the real life we have a lot of factors that can change some of the variables for the model on this case.