Consider the following income tax scheme: The first $6.000 of income is not subject to any tax The next $10.000 is subject to a tax rate of 20% The next $30.000 is subject to a tax rate of 30% Any additional income subject to tax rate of 40% a. Find and graph the tax function T(y), defined on y ? 0 b. Determine the points of nondifferentiability for those function and why each is a point of nondifferentiability c. Graph the marginal tax function and the average tax function ((T(y))/y)^
Added by Tiara A.
Step 1
To find the tax function T(y), we need to consider the different income ranges and their respective tax rates: Show more…
Show all steps
Close
Your feedback will help us improve your experience
Georgiann Andersen and 59 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In a certain country, income tax is assessed as follows. There is no tax on income up to 10,000 dollars. Any income over 10,000 dollars is taxed at a rate of 10%, up to an income of 20,000 dollars. Any income over 20,000 dollars is taxed at 15%. (a) Sketch the graph of the tax rate $ R $ as a function of the income $ I $. (b) How much tax is assessed on an income of 14,000 dollars? On 26,000 dollars? (c) Sketch the graph of the total assessed tax $ T $ as a function of the income $ I $.
Functions and Models
Four Ways to Represent a Function
Income Tax In a certain country, income tax $T$ is assessed according to the following function of income $x :$ $$r(x)=\left\{\begin{array}{ll}{0} & {\text { if } 0 \leq x \leq 10,000} \\ {0.08 x} & {\text { if } 10,000 < x \leq 20,000} \\ {1600+0.15 x} & {\text { if } 20,000 < x}\end{array}\right.$$ \begin{equation} \begin{array}{l}{\text { (a) Find } T(5,000), T(12,000), \text { and } T(25,000) .} \\ {\text { (b) What do your answers in part (a) represent? }}\end{array} \end{equation}
Functions
Income Tax In a certain country, income tax $T$ is assessed according to the following function of income $x$ : $$ T(x)=\left\{\begin{array}{ll}{0} & {\text { if } 0 \leq x \leq 10,000} \\ {0.08 x} & {\text { if } 10,000<x \leq 20,000} \\ {1600+0.15 x} & {\text { if } 20,000<x}\end{array}\right. $$ $$ \begin{array}{l}{\text { (a) Find } T(5,000), T(12,000), \text { and } T(25,000)} \\ {\text { (b) What do your answers in part (a) represent? }}\end{array} $$
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD