Download Exponential Function

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]