MCS 119 Spring 2013
March 7, 2013
MCS 119, 3/7/13
Announcements
•  Tutors are on duty, Sun – Thurs, 6:30 -9:30, Olin 329
•  Homework due today.
•  The study guide for exam 1 has been posted on the course web
page.
•  While we will have an optional review session during class time
next Thurs., we strongly recommend that you start studying now.
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Today’s schedule
•  Quick review of exponential growth problems
•  Half-life
•  Sound levels/intensity
•  Problem that can’t be solved using logs
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Compound interest
A $5000 investment earns 7.2% annual interest, and an
$8000 investment earns 5.4% annual interest, both
compounded continuously. How long will it take for the
smaller investment to catch up with the larger one?
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Exponential decay and half-life
Sodium-24 is a radioactive isotope of sodium that is used
to study circulatory dysfunction. Assuming that 4
micrograms of sodium-24 is injected into a person, the
amount A in micrograms remaining in that person after t
hours is given by the equation A = 4e-0.046t. What amount
of sodium remains after 5 hours? What is the half-life of
sodium-24?
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Blood alcohol
A person’s blood alcohol content is a measure of how
much alcohol is in the blood stream. When a person
stops drinking, the BAC declines over time as the alcohol
is metabolized. The BAC, Q, of a person t minutes after
he stops drinking is given by
Q = Q0 e−t/τ
Where Q0 is the initial BAC and τ is the elimination time.
How long does it take for a person’s BAC to drop from
0.10 to 0.04 if the elimination time is 2.5 hours?
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Sound intensity
The intensity of sound varies over an enormous range,
and thus we use a logarithmic scale to measure sound.
Then noise level in decibels is given by the formula
Noise level in decibels = 10log(I/I0)
where I0=10-16 watts/cm2, the lowest sound still audible
to humans.
Loud music can measure 110 dB whereas normal
conversation measure 50 dB. How many times more
intense is loud music than normal conversation?
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Problems that can’t be solved with logs
The population of a country (in millions) is given by the
formula P=2(1.02)t, where t is years. The food supply, in
terms of millions of people that can be fed, is given by N
= 4 +0.5t. Determine the year in which the country first
experiences food shortages.
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 119, 3/7/13
Coming up:
•  Graphing logarithmic functions tomorrow
•  Finding maximum values of functions Mon. and Tues.
•  Test on Thurs. evening
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu