Question

a videoke machine can be rented for 1000 for three days but for the fourth day onward an additional cast Php 40 per day s added represent the cast of renting a videoke machine as a piecewise function of the number of days rentin

Answer 1

Given : a videoke machine can be rented for 1000 for three days but for the fourth day onward an additional cast Php 40 per day s added

To Find : represent the cost of renting a videoke machine as a piecewise function of the number of days renting

Solution:

d = number of days

f(d) = cost

videoke machine can be rented for 1000 for three days

Rented Days can not be Negative   or zero

f(d)  = 1000    0 < d  ≤ 3

for the fourth day onward an additional cast Php 40 per day

=> f(d)  = 1000 + 40(d-3)    3 < d

=> f(d)  = 1000 + 40d  - 120   3 < d

=>  f(d)  =  4d + 880    3 < d

Piece wise function

f(d)  = 1000    0 < d  ≤ 3  

          4d + 880    3 < d

$f(d) = \left \{ {{1000 \quad 0<d\leq3} \atop {4d+800 \quad 3<d}} \right.$

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