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Transcript
Section 3.3 1. Use a calculator to evaluate, rounding to three decimal places. a. e 2 b. e -2 c. e ½ 2. Express as a power of e a. 5 e e 3. Graph y = 3 -2 x b. c. e5 e3 e 5e 1 e 2e on a graphing calculator. 4. Graph y = (1/3) on a graphing calculator. x 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). a. How much will you owe after 3 years? b. 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 zerocoupon $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: a. 4 years b. 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) Find the probability if a meltdown: a. within 25 years. 100n . 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 36e 22e 0.019x 0.013x and the population of Texas will be (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]