Example 1
A person will choose a health plan between two options: A and B.
Plan conditions:
Plan A: charges a fixed monthly amount of R$140.00 and R$20.00 per appointment within a certain period.
Plan B: charges a fixed monthly amount of R$110.00 and R$25.00 per appointment within a certain period.
We have that the total expense of each plan is given as a function of the number of appointments x within the pre-established period.
Let's determine:
a) The function corresponding to each plane.
b) In which situation plan A is more economical; plan B is more economical; the two are equivalent.
a) Plan A: f (x) = 20x + 140
Plan B: g (x) = 25x + 110
b) For plan A to be more economical:
g (x) > f (x)
25x + 110 > 20x + 140
25x - 20x > 140 - 110
5x > 30
x > 30/5
x > 6
For Plan B to be more economical:
g(x) < f(x)
25x + 110 < 20x + 140
25x – 20x < 140 – 110
5x < 30
x < 30/5
x < 6
For them to be equivalent:
g(x) = f(x)
25x + 110 = 20x + 140
25x - 20x = 140 - 110
5x = 30
x = 30/5
x = 6
The most economical plan will be:
Plan A = when the number of consultations is greater than 6.
Plan B = when the number of consultations is less than 6.
The two plans will be equivalent when the number of queries is equal to 6.
Example 2
In the production of parts, a factory has a fixed cost of R$16.00 plus a variable cost of R$1.50 per unit produced. Where x is the number of unit parts produced, determine:
a) The law of function that provides the cost of producing x pieces;
b) Calculate the production cost of 400 pieces.
Answers
a) f (x) = 1.5x + 16
b) f (x) = 1.5x + 16
f (400) = 1.5*400 + 16
f (400) = 600 + 16
f (400) = 616
The cost to produce 400 pieces will be R$ 616.00.
Example 3
A taxi driver charges R$4.50 with a fare plus R$0.90 per kilometer traveled. Knowing that the price to pay is given as a function of the number of kilometers traveled, calculate the price to be paid for a race in which 22 kilometers were covered?
f (x) = 0.9x + 4.5
f(22) = 0.9*22 + 4.5
f(22) = 19.8 + 4.5
f(22) = 24.3
The price to pay for a race that covered 22 kilometers is R$ 24.30.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Source: Brazil School - https://brasilescola.uol.com.br/matematica/aplicacoes-uma-funcao-1-grau.htm