Download Algebra 2B - Barrington 220

Algebra 2B
So, when are
we ever gonna
use this?
Name ____________________________________
Applications of Exponential and Logarithmic Functions
1) Medicine - Bacteria Growth: Cholera, an intestinal disease, is caused by cholera bacterium that multiply exponentially by
1.386t
cell division, as modeled by the equation A  Ne
, where N is the original number of bacterium, and A is the amount of
bacteria after t hours. If we start with 1 bacterium, how many are present after….
a) 5 hours?
b) 12 hours?
c) How many hours will it take for there to be 1 million bacteria?
2) Psychology: Educational psychologists sometimes use mathematical models of memory. Suppose a group of students take a
chemistry test. After some time, without review of the material, they take an equivalent form of the same test. The
mathematical model describing the students’ retention of the material is a  12 log(t  1)  82 , where a is the average score
at time t days.
a) What was the average score when the
b) What is the average score after 6 days?
students first took the test (t=0)?
b) After how many days is the average score 60?
3) Carbon-14 Dating: Plants absorb carbon dioxide from the atmosphere, and animals obtain carbon from the plans they
consume. When a plant or animal dies, the amount of carbon-14 it contains decays exponentially according to the equation
N  N 0 e 0.00012t , where N= is amount of carbon present after t years, and N0 is the original amount of carbon. If a bone is
found to contain 50% of its original carbon-14, how old is the bone?
Finance: Use the equations
 r
A  P 1  
 n
nt
or
A  Pe rt
4) A promissory note will pay $30,000 at maturity 10 years from now. How will you need to pay for the note now if it gains
9% interest, compounded continuously?
5) How long will it take $3000 to double if it is invested at 3% interest, compounded monthly?
6) How long will it take $20,000 to become $30,000 if invested at 4.5% interest, compounded continuously?
Algebra 2B
Applications of Exponential and Logarithmic Functions HW D4
Name ____________________________________
1) Geology: The earth’s atmospheric pressure changes as you rise above the surface. At an altitude of h kilometers, the
0.116 h
pressure, P in newtons per square centimeter is approximately modeled by P  10.13e
.
a) What is the atmospheric pressure at the earth’s surface?
b) What is the atmospheric pressure at the top of Mt. Everest, which is 8.85 km above the earth’s surface?
2) Medicine – Wound Healing: The normal healing of wounds can be modeled by the equation A = A0e -0.3t , where A0 is the
original area of the wound and A is the area of the wound after t days. If the wound initially had an area of 100 mm2,
a) How large is the wound after 3 days?
b) How many days will it take the wound do become 10 mm2?
3) Acoustics: The number of decibels of sound, D, can be given by the equation D  10 log( I )  160 , where I is the power of
sound, measured in watts. The loudest sound made by any animal is made by the blue whale and can be heard over 500 miles
away. If the power of sound of the blue whale is 630 watts, find the number of decibels emitted.
4) Carbon-14 Dating: A wooden chest is found and is claimed to be from the second century B.C.E. Test on a sample of
wood from the chest reveal that it contains 92% of its original carbon-14. How old is the chest? Could the test be from the
second century B.C.E? (Formula:
amount of carbon.
N = N oe-0.00012t , where N= is amount of carbon present after t years, and N0 is the original


Be careful of WHAT you are solving for! Use the formula A  P  1 
r

n
nt
or A  Pe
rt
for the following problems.
5) Suppose you want to invest $1500 at an annual interest rate of 6.5%. What would your investment be worth at the
end of 10 years if the interest is compounded
a)monthly?
b) continuously?
6) How much money would have to be invested at 7.5% interest compounded continuously, in order to end up with
$3000 and the end of 3 years?
7) How much money would have to be invested at 6% interest, compounded quarterly, in order to end up with $5000 at the end
of 7 years?
8) $2000 is invested at 8% interest, compounded semi-annually. How long will it take the investment to double?
9) $5000 is invested at 9% interest, compounded continuously. How long will it take the investment to triple?