Review questions for test on logarithms and exponents.

1. What does exponential growth look like?
Slide23

2. 1. Find the domain and range of ƒ.
2. Find the equation of the asymptote if there is one.
3. Find the x and y intercepts of the graph of ƒ if there are any.
4. Sketch the graph of ƒ.

3. 1. Find the domain and range of ƒ.
2. Find the equation of the asymptote if there is one.
3. Find the x and y intercepts of the graph ƒ if there are any.
4. Sketch the graph of ƒ.

4. Expand ... Simplify ...

5. At the begining of an experiment a colony of flibberdejibbets has 2 million
members. After 4 hours the population has increased by 20%. At that time a
biologist, Dr. Trapper John, treats the colony with an agent that slows the
colony’s rate of growth. At the new growth rate, the colony takes three times as
long to double in size as at the old growth rate. How long after the treatment
with the size of the colony of flibberdejibbets reach 12 million?
YOU MAY USE THE REST OF THESE
PROBLEMS AS REVIEW EXERCISES
The answer is here ...
ANSWER: 106 hours

6. An amount of $3,000.00 is deposited in a bank paying an annual interest rate of
3 %, compounded continuously.
(a) Find the balance after 4 years.
(b) How long would it take for the money to double?

7. At the present time, there are 1000 type A bacteria. If the rate of increase
per hour is 0.025, how many bacteria can you expect in 24 hours?

8. A radioactive substance decays at a daily rate of 0.13. How long does it take for
this substance to decompose to half its size?

9. In 1999, the population of Winnipeg was 630 700, and was increasing at the rate
of 0.54% per year.
(a) Write an equation to represent the population of Winnipeg, P, as a
function of the number of years, y, since 1999.
(b) Calculate how many years it would take for the population to double.
(c) Calculate when the population will reach 1 million.
(d) Write the equation in part (a) as an exponential function with base 2.
(e) Write the equation in part (a) as an exponential function with base e.