Download 4.1 Exponential Functions

Section 4.1
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. Athletic Olympic Games: - When the Olympic Games were held in Mexico
City in the summer of 1968, many athletes were concerned that the high elevation
would effect there performance. IF air pressure decreases exponentially by 0.4%
for each 100 feet of altitude, by what percentage did the air pressure decrease by
moving to Tokyo (the site of the 1964 Summer Olympics, at altitude 30 feet) to
Mexico city (altitude 7347 feet)?
15. 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]