Exam 4: Functions Given by Words

There are 19,077 students at your university.The student population is expected to grow by 7% per year for the next few years.What is the expected student population after 3 years? Round your answer to the nearest whole number. ​

You start with an investment of $1440.09.The first year the investment grows by 7%.The second year the investment declines by 7%.What is the value of the investment at the end of the two-year period? Round your answer to the nearest cent. ​

Sugar costs $1.55 per pound, and lemons cost $0.47 each.You sell lemonade for $1.35 per glass.Write S for the pounds of sugar used, L for the number of lemons used, G for the number of glasses of lemonade you sell, and P for the profit, in dollars, you make.Express using a formula your profit in terms of pounds of sugar used, number of lemons used, and number of glasses of lemonade sold. ​

You sell cookies for 84 cents each.You paid $9.85 for ingredients to make the cookies.Which of the following is a correct formula for the profit P, in dollars, you make from baking and selling c cookies? ​

If you are driving at a constant speed, the distance you travel is proportional to the time you spend driving.Using D for the distance traveled, in miles, t for the time, in hours, that you drive, and r for the constant of proportionality, express the proportionality relation using a formula. ​

The weight of a pizza with fixed diameter is proportional to its thickness.

When formulas are used to represent verbal descriptions, it is important to write down what the variables represent.

If you work for $8 per hour, then your pay P, in dollars, is proportional to the hours you work.Express this proportionality relationship as a formula using H for hours worked. ​

A woman's height is proportional to her age.

It takes 13 minutes to preheat your oven.Once the oven is preheated, baking time for a roast is 13 minutes per pound.Using w as the weight of the roast, in pounds, and B for oven time (including preheating time), in minutes, give a formula that shows the oven time for a roast that weighs w pounds. ​

The area of a square is proportional to the length of a side.

You start with $32.28 in your piggy bank and add $9.28 each week.Write a formula for the amount P of money, in dollars, in your piggy bank after t weeks. ​

The temperature of an oven remains constant at 391 degrees Fahrenheit.A potato is placed in the oven to bake.The difference between the temperature of the oven and that of the potato after t minutes in the oven is given by degrees Fahrenheit.Write a formula that gives the temperature T, in degrees Fahrenheit, of the potato after t minutes in the oven. ​

An initial investment of $545.45 declines at a rate of 5 percent per year.What is the value of the investment after 3 years? Round your answer to the nearest cent. ​ ​

If a formula does not match a verbal description at one point, the formula and verbal description may still describe the same function.

When variables are introduced to describe real situations, it is important to include proper units.

In a proportionality relationship, the constant of proportionality varies with time.

The maximum length of a certain type of fish is 61 centimeters.The difference between the maximum length and the length at age t years is given by centimeters.Write a formula that gives the length L, in centimeters, of the fish at age t years. ​

If I make $23 per hour then my pay is proportional to the hours I work.

Verifying agreement at several points assures that a verbal description and a formula describe the same function.