8/11/2019 Business Cal, Test 1

1/4

Name:

Math 122 Test 1

Directions: Please write your answers, with all appropriate work, in the spacesprovided. Answers given without work shown will be counted incorrect. You may usethe backs of the pages if you require some space for scratchwork or brainstorming.

1. Write each of the following in interval notation.

(a) 1 x

8/11/2019 Business Cal, Test 1

2/4

4. What is the relative change in the price of given a $1 increase?

(a) a concert ticket at $50

(b) chocolate at $3

5. Suppose a toy company has a $1000/day fixed operating cost, that their toys cost$2 each to produce, and that they sell their toys for $10 each. What is their dailyprofit function, and what number of toys define their break-even point?

6. Suppose that the supply and demand functions for orange beanies are, respectively,S(p) = 10pand D(p) = 10020p. Now suppose that a 5% sales tax is placed uponconsumers. Find the equilibrium price and quantity after the imposition of the tax.

2

8/11/2019 Business Cal, Test 1

3/4

7. A certain radioactive clam has a half-life of 101 years. Write an exponential functiondescribing the amount of radioactive material left after t years given that P ouncesare present at t= 0.

8. What is the future value of $100 after 100 years in an account that yields 5% interestcompounded monthly?

9. The momentum of an object is directly proportional to the square of its velocity.Write an equation describing this relationship (be sure to indicate the meanings ofyour variables).

3

8/11/2019 Business Cal, Test 1

4/4

10. Given f(x) = 2x2, estimate f(2). Show a few steps.

4