advertisement

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