Exam 1: Functions Given by Formulas

The only valid way of presenting a function is with a formula.

For functions that model practical phenomena, the variables involved often have units associated with them.

The functional notation means .

If represents the cost of purchasing b burgers, f orders of fries, and d drinks, then represents 10 burgers, 6 orders of fries, and 12 drinks.

Let denote the monthly payment if you borrow P dollars at an APR of A percent, and the loan is repaid in t months.Use functional notation to indicate the monthly payment if you borrow 5532 dollars at an APR of 4.22 percent, and you repay the loan in 4 years.

If , calculate the value of . ​

If represents the library charges on b books that are w weeks overdue, explain in practical terms the meaning of .

If , calculate the value of . ​

The distance, in miles, from me to a moving train is given by . ​ Here t represents hours since I heard the train whistle.Calculate the distance to the train 5 hours after I heard the whistle. ​

In the event of an emergency stop, the speed S, in miles per hour, of a car when brakes are applied can be calculated from the length L, in feet, of skid marks.The relationship is .Suppose skid marks are 67.40 feet long.Use functional notation to express the speed of the car, and then calculate that value. ​

Let denote the monthly payment if you borrow P dollars at a monthly rate of r expressed as a decimal, and the loan is repaid in t months.Use functional notation to indicate the monthly payment if you borrow 5726 dollars at an APR of 9.44 percent, and you repay the loan in 5 years.Use 3 decimal places for r.

If represents federal defense spending t years after 2000, then represents federal defense spending in 2012.

A water source is contaminated with a toxic chemical and is being cleaned.The amount of chemical, in grams, remaining t hours after the cleaning process began is given by ​ . ​ How much of the chemical is removed from time to time ? ​

Let denote the price in dollars of p pizzas, s sodas, and c bags of chips.Use functional notation to indicate the cost of 5 pizzas, 4 sodas, and 4 bags of chips.

If represents the value of a car t years after it is purchased from the dealer, then indicates the value of the car on the showroom floor.

If , calculate the value of . ​

Let denote the balance, in dollars, of an account t months after the account is opened.Use functional notation to indicate the balance of the account after 2 years and 11 months.

If , calculate the value of .Round your answer to two decimal places if necessary. ​

Let denote the traffic fine, in dollars, associated with driving m miles per hour over the speed limit.Explain in practical terms the meaning of .

The functional notation means the function whose name is evaluated at .