SOLUTION: The Topology Taxi Company charges 2.30 for the first quarter of a mile and 0.55 for each additional quarter of a mile. Find a linear function which models the taxi fare F as a func

Question 1152410: The Topology Taxi Company charges 2.30 for the first quarter of a mile and 0.55 for each additional quarter of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven, m.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
best single function i could come up with is:

y = 2.2 * x + 1.75

the graph of that funcion for the first 2 miles is shown below:

$$$

from this graph, you can see that the first quarter mile costs 2.2 * .25 + 1.75 = 2.30

each additional quarter mile after that costs an additional .55.

for example, the second quarter mile costs 2.30 + .55 = 2.85.

the function is written as y = 2.2 * x + 1.75 so it can be graphed.

as graphed, x represents the total miles driven and y represents the total cost of the trip.

it can also be written as f(m) = 2.2 * m + 1.75

with the function named as such, m represents the total miles driven and f(m) represents the total cost of the trip.

in the functional notation format, f is the name of the function and m is the argument of the function.

here's a couple of references on functional notation you might find helpful.

https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html

https://www.purplemath.com/modules/fcnnot.htm

the procedure in solving this problem was this:

the cost per quarter mile is .55
multiply that by 4 to get a cost per mile of 2.20.
this will be the cost for every mile, except the first mile.
the cost for the first mile will be difference because the cost of the first mile is 2.30 rather than .55
the difference between 2.30 and .55 is 1.75.
that is added to the total cost.
the 1.75 represents the 0 mile cost.
when the person gets in the cab, the meter will charge 1.75 + .55 for every quarter mile driven.
the first quarter mile costs 2.30, the second 2.85, which is .55 more, etc., as shown on the graph.

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