3 log
exponential and
A Birt 1,000 deposits is made at a bank that pays 12% interest compounded
monthly. How much will be in the account at the end of 10 years?
4
If you start a Biology experiment with 5,000,000 cells and 25% of the cells are
dying every minute, how long will it be before there are fewer than 1,000 cells?
5 Learning curve: In psychological tests, it is found that students can memorize a
list of words after 1 hours, according to the learning curve y = 50 – 50e -031
where
y is the number of words a student can learn during the rh hour of study. Find how
many words a student would be expected to learn in the ninth hour of study.
6 The energy released by the largest earthquake recorded, measured in joules, is
about 100 billion times the energy released by a small earthquake that is barely
felt. In 1935 the California seismologist Charles Richter devised a logarithmic
scale that bears his name and is still widely used. The magnitude M on the Richter
scale is given as follows:
E
Richter scale
E.
where E is the energy released by the earthquake measured in joules, and Eo is the
energy released by a very small reference earth quake which has been
standardized to be E. = 10440 joules.
Question:
An earth quake in a certain town X released approximately 5.96 x 10 joules of
energy. What was its magnitude on the Richter scale? Give your answer to two
decimal places.
7 Physics: The basic unit of sound measurement is called a bell, named after the
inventor of telephone, Alexander Graham Bell (1847-1922). The loudest sound a
healthy person can hear without damage to the eardrum has an intensity I trillion
(10'3) times that of the softest of sound a person can hear. The relationship of
loudness of sound L and intensities I and I. is given by
1
L=10log
ī
M =
3
Oom
and te
atory. lat
y mind
100,00
ved that
where L is measured in decibels, /, is the intensity of the least audible sound that
an average healthy person can hear, which is given by 10-12
wall per square meter,
and I is the intensity of the sound in question.
Question: Find the number of decibels:
from an ordinary conversation with sound intensity I = 3.2 x 100 watt per
square meter.
from a rock music concert with sound intensity I = 5.2 x 10 watt per square
centimetre.
1103
а
b
10.​