BITI 1223 Calculus & Numerical Methods
Faculty of Information and Communications & Technology
Tutorial 2: Exponential and Logarithm Functions
1.
Simply the following expression.
a.
b.
c.
d.
2.
Solve the following functions.
a.
b.
c.
1.
2.
Express the following logarithms in terms of ln 5 and ln 7.
a.
ln (1/125)
b.
ln
c.
[ln 35 + ln (1/7)]/(ln 25)
Use the properties of logarithms to simplify the following expressions.
a.
3.
√
ln
b.
ln
c.
3 ln √
ln (
)
ln 2
ln (t + 1)
Find simpler expressions for the following quantities.
a.
b.
c.
d.
BITI 1223 Calculus & Numerical Methods
Faculty of Information and Communications & Technology
4.
Solve for y
a.
b.
c.
d.
e.
5.
The number of bacteria cells in a liquid culture at the beginning of the experiment was
10,000 and after 3 hours there are 500,000 cells. ( Hint: The growth of bacteria is given
by the function
, where
is the initial population, t is time and k is a
constant).
a.
How many bacteria will there be after 1 day?
b.
How long does it take for the bacteria to double its initial population?