Download 1) - Catalyst

1) Suppose a savings account pays 5% interest per year, compounded four times per
year. If the savings account starts with $600, how many years would it take for
the savings account to exceed $2000?
2) If you borrow $500 from a credit union at 12% annual interest and $250 from a
bank at 18% annual interest, what is the effective annual interest rate (that is, what
single rate of interest on $750 would result in the same total amount of interest)?
3) Suppose a radioactive isotope is such that five-sixth of the atoms in a sample
decay after four days. Find the half-life of this isotope.
4) A salesperson finds that her sales average 40 cases per store when she visits 20
stores a week. Each time she visits an additional store per week, the average sales
per store decrease by 1 case. How many stores should she visit each week if she
wants to maximize her sales?
5) You have already invested $550 in a stock with an annual return of 14%. How
much of an additional $1100 should be invested at 12% and how much at 6% so
that the total return on the entire $1650 is 9%?
6) How much would you need to deposit in a bank account paying 5% annual
interest compounded continuously so that at the end of 15 years you would have
$20,000?
7) A radiator contains 8 quarts of fluid, 40% of which is antifreeze. How much fluid
should be drained and replaced with pure antifreeze so that the new mixture is
60% antifreeze?
8) Suppose a colony of 50 bacteria cells has a continuous growth rate of 35% per
hour. Suppose a second colony of 300 bacteria cells has a continuous growth rate
of 15% per hour. How long does it take for the two colonies to have the same
number of bacteria cells?
9) An airplane flew with the wind for 2.5 hours and returned the same distance
against the wind in 3.5 hours. If the cruising speed of the plane was a constant
360 mph in air, how fast was the wind blowing?
10) An advertisement for real estate published in the 26 July 2004 electronic edition
of the New York Times states:
Did you know that the percent increase of the value of a home in
Manhattan between the years 1950 and 2000 was 721%? Buy a home in
Manhattan and invest in your future.
Suppose instead of buying a home in Manhattan in 1950, someone had invested
money in a bank account that compounds interest once per month. What annual
interest rate would the bank have to pay to equal the growth claimed in the ad
from the previous exercise?
11) The Golden Gate Bridge is supported by two huge cables strung between the
towers at each end of the bridge. The function
f ( x)  .0001193x 2  .50106 x  526.113
gives the approximate height of the cables above the roadway at a point on the road x
feet from one of the towers. The cables touch the roadway halfway between the two
towers. How far apart are the towers?