Function Situtations?

Question

"Define variables and write a function that describes each situation.

a. You drive on an interstate highway with your cruise control set at 65 MPH and do not need to stop or alter your speed.

b. You rent a small moving van to move your belongings to your new apartment. The rental company charges $45 a day plus $0.22 a mile to rent the van."

Please explain too.. thanks!

Answer 1

So essentially you want a statement that expresses each of these situations in words.

a. I'm assuming this question wants a function for speed. Nothing changes in the problem so we don't have to worry about time, etc.

so we have v = speed (pick any letter you like; v is traditional for velocity)
Since it's always the same:
v = 65 (regardless of anything else).

b. This one it changes. The three variables (things that "vary") are the price charged (let's call it p for price); the number of days (d), and the number of miles (m).

You have that the company charges $45 for each day, so the price from there is 45*d. They also charge 22 cents a mile, so the price is 0.22*m.

So the total price, p, is (price because of days) + (price because of miles):
p = 45*d + 0.22*m.

Answer 2

a) There is no function that I can see so just start off by defining your variables. In this case your only variable is a constant Speed=S=65MPH

b) This could be a funtion if you want to determine how much you will spend on a van. A function is used to figure something out. If there is nothing to figure out or calculate such as in question a then you do not have a function. Here the function is total cost equals the day rental plus the milage. In math terms we have Total= Day Rental+ (Cost Per Miles*Miles driven) or Total (t)= $45 (Day rental Fee as per above)+ $.22(Coste per mile)*m (Miles driven)
t=$45+$.22m

Answer 3

a.
Let t = time, v = speed, x = distance.
Since v is the time derivative of x (v = dx/dt), it follows that the total distance traveled is (dx/dt)dt = vdt (chain rule). Integrating both sides: x = vt + c where c is an arbitrary constant that specifies the starting position. So, you could write it as a function like x(v,t) = vt+c. I'm assuming that the distance is what you want to find...

b.
cost(days,miles) = 45*days + 0.22*miles. Trivial on inspection.

Answer 4

Variables are things that change.

Functions are equations that describe how things will change.

So:

a) Define variables:

x = Cruise control setting

Function: x = 65.

b) Define variables:

x = Days rented
y = Miles driven

Function:

Cost = $45x + .22y

Answer 5

Just fly it alot faster!