1. In a company, the salaries of part-time employees are calculated as follows: An employee is paid $15 per hour for the first 20 hours. For every additional hour until the total hours add up to 30, they will be paid $18. If their workload exceeds 30 hours per week, they will be paid $20 per every additional hour over 30. (a) Write a function S(r) that gives the weekly salary of an employee where a is the number of hours worked. (b) Graph S(r) either by hand or through "desmos.com". (c) Evaluate the following: i. lim-20- S(x). ii. lim-20+ S(x). iii. lim-20 S(r). iv. S(20). v. limx→30- S(x). vi. lim, 30+ S(x). vii. lim, 30 S(r). viii. S(30). ix. lim-40- S(x). x. limx→40+ S(x). xi. lim-+40 S(x). xii. S(40). (d) Using your answers above find all values on the interval (0, 40) where the function S is discontin- uous (if there are any.) Identify the types of discontinuity.
1. In a company, the salaries of part-time employees are calculated as follows: An employee is paid $15 per hour for the first 20 hours. For every additional hour until the total hours add up to 30, they will be paid $18. If their workload exceeds 30 hours per week, they will be paid $20 per every additional hour over 30. (a) Write a function S(r) that gives the weekly salary of an employee where a is the number of hours worked. (b) Graph S(r) either by hand or through "desmos.com". (c) Evaluate the following: i. lim-20- S(x). ii. lim-20+ S(x). iii. lim-20 S(r). iv. S(20). v. limx→30- S(x). vi. lim, 30+ S(x). vii. lim, 30 S(r). viii. S(30). ix. lim-40- S(x). x. limx→40+ S(x). xi. lim-+40 S(x). xii. S(40). (d) Using your answers above find all values on the interval (0, 40) where the function S is discontin- uous (if there are any.) Identify the types of discontinuity.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. In a company, the salaries of part-time employees are calculated as follows: An employee is paid $15
per hour for the first 20 hours. For every additional hour until the total hours add up to 30, they will
be paid $18. If their workload exceeds 30 hours per week, they will be paid $20 per every additional
hour over 30.
(a) Write a function S(r) that gives the weekly salary of an employee where a is the number of hours
worked.
(b) Graph S(r) either by hand or through "desmos.com".
(c) Evaluate the following:
i. lim-20- S(x).
ii. lim-20+ S(x).
iii. limx→20 S(x).
iv. S(20).
v. limx→30- S(x).
vi. lim, 30+ S(x).
vii. lim 30 S(r).
viii. S(30).
ix. lim-40- S(x).
x. limx→40+ S(x).
xi. lim,—40 S(r).
xii. S(40).
(d) Using your answers above find all values on the interval (0,40) where the function S is discontin-
uous (if there are any.) Identify the types of discontinuity.
2. A postal service company applies the following rates for a certain carriage service. If the package
weighs no more than 5 lb, they charge a flat rate of $20. If the package weighs more than 5 lb, but no
more than 10 lb, they charge a flat rate of $30. If the package weighs more than 10 lb, but no more
than 20 lb, they charge a flat rate of $40. If the package weighs more than 20 lb, but no more than
30 lb, they charge a flat rate of $50. If the package weighs more 30 lb, the package needs to be send
through a different service.
(a) Write a function p(r) that gives the price of a package that weighs x lb.
(b) Graph p(x) either by hand or using "desmos.com".
(c) Identify the discontinuities of the function (if there are any.) Identify the types of discontinuity.
Expert Solution
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1.
The salary of a part-time employees are calculated as,
An employee is paid per hour for the first hours.
For every additional hour until the total hours add up to , they will be paid .
If their work exceeds hours per week, they will be paid per every additional hour over .
We have to write a salary function and find the given values.
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