MCR 3U Exponential Functions Test

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Equivalent
MCR 3U Grade 11 University
Exponential Functions TEST 11
Weighted Mark: _ _ _ _ _%
Thinking, Inquiry & Problem Solving
Knowledge & Understanding
Application
Communication
Knowledge & Understanding
1. Evaluate: [K 12]
𝟐
−𝟑
a) (𝟑𝟐𝟎.𝟒 ) (𝟐𝟕 ) ÷
𝟑
𝟏𝟔 𝟒
( )
𝟖𝟏
/9
/ 32
/6
/4
𝟑 −𝟏
b) (𝟎. 𝟑)−𝟑 + ( )
𝟕
c)
𝟏
𝟏 −𝟐
(𝟒𝟗)
𝟏
𝟏 −𝟑
− (𝟖)
𝟐
(𝟔𝟒)𝟑
𝟏 −𝟎.𝟓
+ (−𝟎. 𝟓)−𝟐 (𝟎. 𝟕𝟓) + (−𝟏)−𝟖 ( )
𝟑𝟔
𝟑
d)
(𝟖𝟎.𝟓 )( √𝟗)
𝟓
(𝟑𝟑 )(√𝟐)
2. Simplify the following expressions: [K 9]
𝟏
𝟏
𝟏 𝟑 𝟏 𝟐
(𝒙𝟐 ) (𝒚𝟒 )
a)
𝟏
𝟑
𝟏 𝟐 𝟏 𝟐
−
(𝒙 𝟑 ) (𝒚𝟑 )
𝟓
b)
𝟏
−
𝒂𝟑 ∙ 𝒃 𝟔
𝟏
−
(𝒂 𝟑
∙
𝟏 𝟒
𝒃𝟑 )
𝟓
(𝒙𝟐.𝟔 )( √𝒚𝟑 )
c)
(𝒙𝟎.𝟑 )(𝒚−𝟎.𝟐 )𝟐
3. Simplify the following expression. State the restriction on the
variables. [K 3]
𝒙𝟎.𝟓 + 𝒃𝟎.𝟓
𝒙𝟎.𝟓
+
𝒚
𝟎.𝟓 −
𝒙 − 𝒙𝟎.𝟓 𝒚
𝒙𝟎.𝟓
𝒙𝟎.𝟓 − 𝒚𝟎.𝟓
4. Given: f (x) = – 2 2x – 4 + 1. State:
a) Domain: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [K 1]
b) Range: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [K 1]
c) x-intercept: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _[K 1]
d) y-intercept: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [K 1]
e) horizontal asymptote: _ _ _ _ _ _ _ _ _ _ [K 1]
f) Graph the function on the grid below: [K 3]
Application
5. The population of a bacteria colony doubles every 20 min. If the
initial population is 250, how many bacteria would be in 3 hours? [A 2]
a
6. The number of yeast cells in a culture grew exponentially from 200 to
6400 in 5 hours. What would be the number of sells in 10 hours? [A 2]
7. The population of a town grows at an annual rate of 2.7 %. How long
will it take for its population to double? [A 2]
Thinking, Inquiry & Problem Solving
8. A cup of hot liquid was left to cool in a room whose temperature was
10o C. The temperature changes according to the function T (t) = 80 ×
𝟏
𝟑𝟎
(𝟎. 𝟓) + 𝟏𝟎.
a) Sketch the graph of the function. [T 3]
b) Explain the meaning of the y-intercept and the asymptote in the
context of this problem. [T 2]
9. An exponential function with a base of 3 has been compressed
horizontally by a factor of 1/2, reflected in the x-axis, and shifted
vertically and horizontally. The graph of the obtained function passes
through the point (1, 1) and has the horizontal asymptote y = 2.
Determine the equation of the obtained function. [T 4]
Communication
10. Compare / contrast the graphs of: [C 4]
a) f (x) = 2x and g (x) = 0.5x
b) f (x) = 0.25 (2x) and g (x) = 2x – 2
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