Question

14.A Zumba instructor charges according to the number of participants, if there
are 10 participants or below, the instructor charge P500.00 for each
participant per month. If the number of participants is between 10 and 25, he
charges P400.00 for each participant per month. If there are 25 participants
or more, he charges P350.00 for each participant per month. Write the
piecewise function that describes what the instructor charges.
if 0 <n < 10
A. 400n if 10 <n S 25
, if n > 35
500n
350n
B.
500n
400n
350n
,if 0 <n <10
,if 10 <n<25
if n = 25
C.
500n
400n
350n
,if 0 <n < 10
,if 10 > n < 25
, if n > 25
D.
500n
400n
350n
,if 0 >n 10
if 10 >n 25
if n <25​

Answer 1

Assume, x represents the number of participants and y be charge per participant.

As y depends on x, we can say,

f(x) = y

For, 0 < x ≤ 10, total charges 500x,

f(x) = 500x , 0 < x ≤ 10

For 10 < x < 25, total charge is 400x,

f(x) = 400x , 10 < x < 25

For x ≥ 25, total charge is 350

f(x) = 350x x ≥ 25

Therefore, we can say,

f(x) = 500x , 0 < x ≤ 10

400x , 10 < x < 25

350x , x ≥ 25

I have written x, you can replace it by n.

Answer 2

Given : .A Zumba instructor charges according to the number of  participants ,

if there are 10 participants or below, the instructor charge P500.00 for each participant per month.

If the number of participants is between 10 and 25, he charges P400.00 for each participant per month.

If there are 25 participants or more, he charges P350.00 for each participant per month.

To Find : Write the piecewise function that describes what the instructor charges.

Solution:

n represent  number of  participants

there are 10 participants or below, the instructor charge P500.00 for each participant per month.

Hence Charges  = 500n            0 < n ≤ 10

If the number of participants is between 10 and 25, he charges P400.00 for each participant per month.

Hence Charges = 400n     10 < n  < 25

If there are 25 participants or more, he charges P350.00 for each participant per month.

Hence Charges = 350n     25 ≤  n  

Hence piecewise function for  charges is :

$\begin{cases}500n \quad 0<n\leq10\\400n \quad 10<n<25\\350n \quad 25 \leq n\end{cases}$

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