Exam 4: Living in a Nonlinear World

Of all the topics we have covered in unit 4, what has stood out to you as something most relevant to your life? Explain why.

The average number of words that can be printed on a standard size piece of paper varies inversely with the font size. a. If 320 words can be printed with a 10-pt size in a particular font, write an equation that relates the average number of words that can be printed to the font size. b. How many words can be printed with a 12-pt size in this font? c. If your teacher tells you to use a 12-pt font, and you decide to try to use a 13-pt font instead, what would you expect to happen in terms of the number of words on the page? (And trust me, your teacher WILL notice that you used that larger font and wider margins. You don't want them in a bad mood when they grade your paper!)

b is inversely proportional to c . If b is 2 when c is 10 , find b when c=5 .

According to the National Association of Realtors, the mean sale price for existing homes in the United States in 2011 was $214,300. Assume that sale prices are normally distributed with a standard deviation of $41,000. Find the percentage of existing homes in 2011 that: b. sold for between $132,300 and $296,300 c. sold for more than $255,300

Find the vertex of the parabola.

A car travels west 8 miles and then north 15 miles. How far is the car from its starting point?

Simplify.

Solve the equation by using the quadratic formula. $3 x ^ { 2 } + 15 x - 72 = 0$

In 2000, the population of Sheboygan, WI was about 113,000 and was growing at a rate of 0.85% per year. Use an exponential function to predict the population in 2023 to the nearest whole number.

Subtract the polynomials. $\left( 4 t ^ { 3 } - 12 t + 6 \right) - \left( - 6 t ^ { 3 } + t ^ { 2 } + 16 t \right)$

Add the polynomials. $\left( 4 w ^ { 2 } + 8 w \right) + \left( 3 z ^ { 2 } - 5 z \right)$

Write the distance formula.

$30,000 is invested in an account that pays 2% simple interest. If the money is invested for 10 years, how much will the account be worth?

If a bank compounds interest quarterly for 10 years, how many total compound periods are there?

Add the polynomials.

Determine whether x and y vary directly, inversely, or jointly in the following equation.

The amount of $6,000 is invested at 5% for 3 years. a. Compute the ending balance if the bank calculates simple interest. b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest?

Simplify the expression. Write the answer in exponent form. $y ^ { 3 } \cdot y ^ { 5 } \cdot y ^ { 7 } \cdot y ^ { 9 }$

Simplify.