MCR3U – Unit 3 TEST
Name
Date
Knowledge
/ 22
Communication
/9
Application
/ 14
__
Thinking
/ 15
Knowledge
1. Simplify by using exponent rules. Answers must only have positive exponents. (2 each)
(c )
[(- c )
4
a.
3 -8
]
!"
b. (64𝑛'( ) #
-2
0.5 4
c. (−3𝑥 ) 𝑝* )(
'+, #
d. / -, $ 0
#'
2. Graph the exponential equation and answer the questions that follow:
(4)
𝒚 = 𝟐(𝟑)(𝒙#𝟐) + 𝟑
a. Identify the y-intercept.
b. Identify the horizontal asymptote.
c. Does this represent growth or decay?
d. Identify the domain:
g. Graph your function.
e. Identify the range:
3. Determine whether the equation represents an exponential function. Explain why? If yes,
determine whether it represents exponential growth or decay, and the rate of
growth/decay. (2 each)
a. 𝑦 = 2𝑥
b. 𝑦 = −2,
. #,
'
c. 𝑦 = ( (0.67),
d. 𝑦 = 6 //0
e. 𝑦 = −3(−2),
Communication
1. Can you determine the equation of the asymptote by looking at an exponential equation?
Justify by stating an example and then state the horizontal asymptote.
(3)
2. Does the table represent an exponential function? Explain your reason why?
(2)
X
y
1
4
2
8
4
32
6
128
7
256
3. State the translation that takes place from 𝑓(𝑥) = 3, to each of the following. (2 each)
)
b. 𝑔(𝑥) = −3(,0)) − 4
a. 𝑔(𝑥) = / 0 3#,
.
Application:
1. The current population of the giant panda is approximately 1600. Suppose the
population is decreasing by 1.5% each year. (6 marks)
a) Does this situation represent exponential growth or exponential decay? How do you know?
b) Identify the initial value, rate of growth/decay and growth/decay factor
Initial Value: ________________
Rate of growth/decay:________________
Growth/decay factor: _____________________
c) Write an equation function to model the number of pandas P(n) depending on the number
of years (n).
2. Anna opened up a savings account with $2,000. The account acquires 0.85% interest
annually. (4 points)
Initial value: _________
Rate of: _________
Growth/Decay
Equation: _______________
3. Suppose a population of 250 crickets doubles in size every 6 months. How many crickets
will there be after 2 years? (4 points)
Thinking:
1. One of the graphs below is an exponential growth and the other is exponential decay. For
each graph, there is a matching table. (2 each)
a. Find an exponential model for table A and B.
Table A: ______________________
Table B: _______________________
2. a. Sketch an exponential growth function whose range is y < -2
b. Sketch an exponential decay function whose range is y > 3
a
b.
(2 each)
3. Simplify the expression Express your answer with positive exponents
(a ) (b )
(a ) (b )
-1
4
1
6
-1
2
-1
-1
3
2
12
4. In the given equation, find the value of x
-2
[4]
2
(
' ,
9∛27; = /-0
[3]