The following situation can be modeled by linear functions. In the following case, draw a graph of the function and use the graph to answer the given question. Be sure you clearly identify the independent and dependent variables. Then briefly discuss whether a linear model is reasonable for the situation described. The cost of a particular private school includes a one-time initiation fee of $\$ 2000$, plus annual tuition of $\$ 10,000$. How much will it cost to attend this school for $6$ years?

Create the required linear function, and use it to answer the following questions.

The Campus Democrats plan to pay a visitor $\$ 100$ to speak at a fundraiser. Tickets will be sold for $\$ 4$ apiece. Find a function that gives the profit/oss for the event as it varies with the number of tickets sold. How many people must attend the event for the club to break even? A $\$ 1200$ washing machine in a laundromat is depreciated for tax purposes at a rate of $\$ 75$ per year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $\$ 0$?

Suppose you have a tablet with a capacity of 16 gigabytes. For a book containing only plain text, 1 byte typically corresponds to one character and an average page contains 2000 characters. Assume all 16 gigabytes are used to hold plain-text books. a. How many pages of text can the tablet hold? b. How many 500-page books can the tablet hold?

For each function, use your intuition or additional research, if necessary, to do the following.

a. Describe an appropriate domain and range for the function.

b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch.

c. Briefly discuss the validity of your graph as a model of the true function.

(minutes after lighting, length of candle)

Competition speed skydivers have reached record speeds of 614 miles per hour. At this speed, how many feet would you fall every second?

The following situation involve a rate of change that is constant. Write a statement that describes how one variable varies with respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer the question. Example: Every week your fingernails grow $5$ millimeters $(\mathrm{mm})$. How much will your fingernails grow in $2.5$ weeks? Solution: The length of your fingernails varies with respect to time, with a rate of change of $5 \mathrm{~mm} / \mathrm{wk}$. In $2.5$ weeks, your fingernails will grow $5 \mathrm{~mm} / \mathrm{wk} \times 2.5 \mathrm{wk}=12.5 \mathrm{~mm}$. Your driverless car maintains a constant speed of $63$ miles per hour along a highway. How far do you travel in $1.5$ hours? In $3.8$ hours?

According to Money magazine, Maryland had the highest median annual household income of any state in $2018$ at $\$75,847$. Assume that annual household income in Maryland follows a normal distribution with a median of $\$75,847$ and standard deviation of $\$33,800$.
a. What is the probability that a household in Maryland has an annual income of $\$100,000$ or more?
b. What is the probability that a household in Maryland has an annual income of $\$40,000$ or less?
c. What is the probability that a household in Maryland has an annual income between $\$50,000$ and $\$70,000?$
d. What is the annual income of a household in the $90$th percentile of annual household income in Maryland?

Write a two-column proof of the Third Angles Theorem.

Use the approximate half-life formula. Discuss whether the formula is valid for the case described.

Urban encroachment is causing the area of a forest to decline at a rate of $7 \%$ per year. What is the approximate half-life of the forest? About what fraction of the forest will remain in $50$ years?

By using the savings plan formula to answer the following question. You want to purchase a new car in $3$ years and expect the car to cost $\$ 30,000$. Your bank offers a plan with a guaranteed APR of $5.5 \%$ if you make regular monthly deposits. How much should you deposit each month to end up with $\$ 30,000$ in $3$ years?

Determine the area of a circular enclosure and a square enclosure made with the given amount of fence. Compare the areas and comment.

$800$ feet of fence

A manufacturer produces 25 -pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deviation?

A parachutist jumps from a plane 11500 ft above the ground. The height, h , in feet, of the parachutist above the ground t seconds after the jump can be modelled by the function h(t)=11500-16t^2 .

a) What type of function is h(t)?

b) What will the parachutist’s height above the ground be after 12 s?

c) When will the parachutist be 1500 ft above the ground?

d) Approximately how long will it take the parachutist to reach the ground?

A manufacturer of lighting fixtures has daily production costs of C = 800 - 10x + 0.25x^2. where C is the total cost (in dollars) and X is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?