Section 3.3

1. Use a calculator to evaluate, rounding to three decimal places.

a. e 2b. e -2c. e ½

2. Express as a power of e

a. e 5 e -2b.c.

3. Graph y = 3 x on a graphing calculator.

4. Graph y = (1/3) x on a graphing calculator.

5. Evaluate e 1.74 using a calculator.

6. BUSINESS: Interest - Find the value of $1000 deposit in a bank at 10% interest for 8 years compounded

a. anually

b. quarterly

c. continuously

7. Personal Finance: Interest - A loan shark lends you $100 at 2% compound interest per week (that is a weekly, not annual rate).

  1. How much will you owe after 3 years?
  2. In “street” language, the profit on such a loan is known as the “vigorish” or the

“vig”. Fins the shark’s vig.

8. Personal Finance: Annual Percentage Rate (APR) - Find the error in the ad shown below, which appeared in a New York paper. [Hint: Check that the nominal rate is equivalent to the effective rate. For daily compounding, s some banks use 365 days and some use 360 days in the year. Try both ways.

At T&M Bank, flexibility is the key word. You can choose the length of time and the amount you deposit, which will earn an annual yield of 9.825% based on a rate of 9.25% compounded daily.

9. Personal Finance: Present Value - A rich uncle wants to make you a million. How much money must he deposit in a trust fund paying 8% compounded quarterly at the time of your birth to yield $1,000,000 when you retire at age 60?

10. Personal Finance: Zero-Coupon Bonds - FUJI Holding recently sold zero-coupon $1000 bonds maturing in 3 years with an annual yield of 10%. Find the price. [Hint: the price is the present value of $1000, 3 years from now at the stated interest rate]

11. General: Compound Interest - Which is better 10% interest compounded quarterly or 9.8% compounded continuously?

12. Personal Finance: Depreciation - A Toyota Corolla automobile lists for $15,450, and depreciates by 35% per year. Find the values after:

  1. 4 yearsb. 6 months

13. General Nuclear Meltdown: - The probability of a “severe core meltdown accident” at a nuclear reactor in the U.S. within the next n years is 1 – (0.9997) 100n.

Find the probability if a meltdown:

  1. within 25 years.b. within 40 years

14. General: Population - As stated earlier, the most populous state is California, with Texas second but gaining. According to the Census Bureau, x years after 2005 the population of California will be 36e0.013x and the population of Texas will be 22e 0.019x (all in millions)

a. Graph these two functions on a calculator on the window [0,100] by [0,150].

b. In which year is Texas projected to overtake California as the most populous state? [hint: use INTERSECT]