Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Metro City's Non-Resident Earnings tax is $6.50$ per thousand dollars of earnings. However, if you earn under $10,000,$ you may subtract $3000$ from your earnings; if between 10,000 and 20,000, you may subtract $2000 ;$ and if between 20,000 and $30,000,$ you may subtract 1000 . So, for example, on 26,000 earnings, you may subtract 1000 and pay tax on 25,000 . Your tax is (25)(6.5)= 162.50 .$ Express the tax $ ,x as a function of x in thousands. Plot the graph. Would you rather earn 19,999(x=19.999) or 20,001 (x=20.001) ?

\begin{array}{l}T(x)=\left\{\begin{array}{cc}6.5 x-19.5 & x<10 \\6.5 x-13 & 10 \leq x<20 \\6.5 x-65 & 20 \leq x<30 \\6.5 x & x \geq 30\end{array}\right. \\T(19.999)=\$ 116.99, T(20.001)=\$ 123.51 \text { rather earn } \$ 19,999\end{array}

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Oregon State University

Baylor University

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

01:25

Graph the indicated functi…

01:24

The distribution of income…

06:19

In a certain country the t…

07:29

In a certain country, inco…

we are going to be using a piece of ice function to determine earnings tax. We are given that this tax is $6.50 per $1000 of earnings. And the limits are that if somebody is earning less than $10,000 they may subtract $3000 from those earnings before taxation. And if they're earning between 10 and $20,000 they can subtract $2000 and if they're earning between 20 and $30,000 they can subtract $1000. This allows us to find the limits of X. Being X must be less than 1000. It was 10,000 X must be less than 10,000. However, we are actually using X in thousands of dollars. So instead of $10,000 it would just be 10. Our next limit is that X must be greater than or equal to 10,000, but less than 20,000. Our final one is that X must be greater than or equal to 20,000, but less than 30,000. To find these limits. We just take a look at what to find the function for the limits. We can see that it is. If you're earning less than 10,000, you pay still 6 50 per $1000 but you can subtract. That's $3000 from your income before that taxation, and that would equate to three times 6 50 which is equal to 1950. And that would be the total tax that you get subtract from your income or from your total taxation, and our next piece gives us that we also have 6 50 per $1000 of income. But this time we're going to be subtracting two times 6 50. She gives us 13, and our next piece is also 6 50 per $1000. But they get to subtract one time 6 50 because they're subtracting that $1000 which equates to just 6 50. That gives us our piecewise function, which describes the earnings income or the earnings tax. Graphically, this would look something similar to this at negative 1950. That's where this would sit going up to 10,000 here. Keeping in mind that are solo is remaining the same in each of these because you can see that our slope is 6 50 for each one of these functions, and it would look something like that. You could graph this on a graphing calculator to get a more accurate picture of it. Um, but moving on, we want to determine, say that we had an income of $19,000.999 or in terms of $1000 for exit would be 19.999 or an X equal to 20.1 Let's determine which one we would prefer for 19.999 We see that falls into our second limit here. So let's plug that in by doing 6 50 times 19.999 It's subtract 13, which gives us a value of 116 0.99 So that's the tax that they would be paying or that we would be paying if our income were 19,999. Now for income word to 20,000 and $1. We would be plugging that into our third function and we would have 6 50 times 20.1 minus 6 50 which gives us a tax that we would have to pay a 123 dollars and 51 cents. Now, glancing at this, we may want to say that we would prefer to make nine good, that we would prefer to make $20,000 because it's more. However, if we take our total income and subtract that tax from it, we'll get what we would actually be left with our after tax income. So let's take our income of $19,999 and subtract the tax that we would have to pay a 116 999 which would give us a final income of 19,000 $882.0 and one cent. Now doing the same for our next piece. We have $20,000.1 in $1 subtracting our tax would have to pay $123.50 and we end up finding that we would be left with an income of 19,000 $877.49 in which case we would actually prefer to have a lower income right here because it allows us to subtract more from what we would pay in taxes, leaving us at the end with a higher income

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:24

A 12 centimeter square sheet of cardboard is to be made into a box by cuttin…

00:55

Determine the value of the logarithm without the use of a calculator.$$\…

01:00

Use your calculator to compute the expression given.$$1.23^{2.5}$$

04:11

A fur dealer finds that when coats sell for $\$ 4000,$ monthly sales are 6 c…

01:57

A 12 inch piece of wire is to be cut into two pieces. One piece is to be use…

01:33

Determine the extrema of the function defined by the equation $f(x)=\frac{x}…

02:36

Find the $x$ -values at which the graph in Exercise 33 crosses its horizonta…

03:59

Use the second derivative test to classify the critical points.$$f(x)=3 …

02:17

Find the dimensions of the largest rectangle with lower base on the $x$ -axi…

01:12

Show that the second derivative test fails for: (a) $f(x)=(x-2)^{3}$ $$\text…