MBF3C – Exponential Relations - Review
1. Evaluate, using a calculator. Round to 3 decimal places where necessary:
(4 marks)
a) 4.923
2.
b) (1.0354)0
c) 7.8-6
Evaluate. Leave answers as fractions and whole numbers.
Decimal answers will be marked 0. (6 marks)
a) (-2)0 =
d) 12-2 =
b) –(20) =
c) (-33)1 =
e) 4-3 =
f) 23 =
3.
Use the exponent rules to simplify the following (leave in exponent form)
(6 marks)
a) 43 x 42
b) (.6)1 x (.6)5
c) 89  85
e)
(102)3
d) (1/4)12  (1/4)7
f) (74)6
4. Evaluate. Leave in exponent form!
(48 ÷ 411) ÷ (42 ÷ 4-8)-3
5. Cells in a culture are growing by a factor of 2.82 per day. The number of cells in the culture, N,
can be estimated using the formula N = 2000(2.82)d, where d is the number of days. (3 marks)
a) How many cells does this culture begin with?
b) How many cells would there be after 1 day?
c) How many cells would there be after 5 days?
Part B: Application
1. An antique that cost $500 is expected to increase in value by 10% each year for 5 years.
a) Create a table of values, showing year and cost (2 marks)
Year
0
Cost($)
500
b) Create an exponential function in the form (y = a x bx) to model the situation.
c) Use your function to find the value of the antique after 50 years.
2. A fossilized snail was analyzed and it was estimated that it originally contained 1.4g of
Carbon 14. The mass of Carbon 14 now is 0.175g. How long ago did the snail live?
(3 marks)
3. The half-life of Bismuth 210 is 5 days. A sample containing 1000mg of this radioactive
element is stored for 20 days. What mass of Bismuth 210 remains?
(2 marks)
4. Graph the relation y = 1 (0.5)x on the graph paper provided. You must draw a graph – not
just a sketch! (4 marks)
Identify the following characteristics of this graph:
a) y-intercept(s) (1 mark)
b) increasing or decreasing? (1 mark)
c) Write the equation of another decreasing graph with a steeper slope.
(1 mark)
Part D: Thinking and Inquiry
1. The half-life of a radioactive element is 2 hours. What fraction of a sample would remain
after 4 hours? (2 marks)
2. The half-life of Sodium 24 is 15 hours. What percentage of a sample would remain after 60
hours? (2 marks)
3. The world’s population in 1978 was about 4.2 billion. Suppose the population increased at
a rate of 2% per year since then. (4 marks)
a) Write an exponential relation that models the problem. Explain what each variable
represents and how you determined the rate value.
b) What will be the world’s population in 2010?
c) What was the population of the world in 1970? What assumptions have you made?