Exponential Functions Test .., I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I I IX

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1 MCT 4C Exponential Functions Test Name: Part A: Fill in the blanks.. Write the following as a single power: (Jii) 8 2. Graph on the grid below as done in class. (a) y = 4(4) Graph y co ordinates between.25 to 2 x 5 (b) y=(2)x [6.. L.L L_J L_J L_J L_J L J_. L j J L_J L_J L J L_J_. :7 5 : : : : : : : : : : : : : : : : :io i- - - # fr 5 q - - fr - fr t- - - j J L_J J L.L.J._.J J A J L_J L_J L_J L_J L_J L L.LU.LJ X Li i..tj... Fill in the chart for the graph in (a): Domain Range x values where x values where x values where x values where Positive (+) Negative ( ) ncreasing Decreasing 4. Exponential functions are written y = ax where a is positive. For what specific values of a are these graphs exponential decay? j4..

2 (c) [x5j = 5 5. implify. No decimal answers. (a) 4x2+8x = ( (b)lo2j. = (d) [_4ab5ja2b5] = 6 2= (e) log 6. During radioactive decay beta particles are released. As beta particles pass through wood their speed decreases to % of the original speed for every metre of wood penetrated. Write an equation representing the percent of the original speed of beta particles P. after passing through d metres of wood. 7. Write in exponential form: og626= 8. Write as a sum & difference of logs: log 24 as a sum: as a difference: 9. Write as a single logarithm. -log 6 2 =

3 Part B: Answer on foolscap. Full solutions are required. how relevant steps as done in class. Finish with a statement for all word problems.. implify. Use steps showing your knowledge of the exponent laws. No decimal answers. (a) 2 (b) 27 (c) [ (d) 4 64 (e) x x 6 x implify the following. how steps for full marks. (a) 92X X+2 27x_ 74 (b) /5x:Y 2xy (c) (5x)2(6x)4 (d) x2 2x2 -x. Evaluate each by writing as a single logarithm first. how steps for full marks. No decimal answers. (a) 4 + log log 4 28 (b) log 27 log 8 (c) log 9 4. olve for x to decimal places. (a) 2x =25 (b) 7X 4X_ 5. n 2 the population of Ayr was. The population increases by 6% every 9 years. (a) Write the equation that represents the population F of Ayr aftery years after 2. (b) Quick sketch the application. Fully label. (c) Using your equation determine the population of Ayr: i) in the year 26 ii) 8 months ago. (d) n what year will the population be million? (e) Write your equation from (a) in logarithmic form. 6. Acetominophen is a head and body ache medication. ts half-life is 94. minutes. An adult dosage is mg. 8 (a) Determine the equation that gives the mass M of acetominophen remaining t minutes after taking an adult dose. (b) Quick sketch the application. Fully label. (c) When will the amount remaining be mg? (Answer to 2 decimal places) 7. There are 2 red ants in a colony. f there were 5 ants in the colony 6 weeks ago 4 what was the daily rate of growth? (Answer as a percent to decimal place) 8. A typical population of bald eagles doubles every 8 years. How many bald eagles are there now if it is predicted there will be 5 in 5 years? 9. An investment of $8 at 6.6% compounded monthly grew to $5. How many years did this take? Answer to 2 decimal places.

4 : Exponential Functions Test Name: AWEi2c. Part A: Fill in the blanks.. Write the following as a single power: (j-) Graph on the grid below as done in class. Graph y co ordinates between.25 to 2 5 (b) y=(2) (a) y=4(4) : : : : : : : : : : : : : : : : : : : : : : : J LJ L_J L_J...L_J L_J L L_.. L :.L :... J L_J L_J.._L_J L_J.L J._L_J_.L_J L_J_.L_J L _L L._ L_j. J_L_J_L..L_J.L_J_. :.5 iii : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -- i :Y: : : :L : : :L : i : :E : i : :E :f: :: ;5*. Fill in the chart for the graph in (a): Domain Range x values where x values where x values where x values where.. Positive (+) Negative ( ) ncreasing 7 Decreasing 4. The graphs in question #2 are examples ofthe graphs y = ax when a > / For what a values are these graphs exponential decay? 4H T

5 . 5. implify. No decimal answers. (a) 4x 2 8x = z - (b) log 2 (c) 2-5 oja T (d) [_4ab5ja2b5 HrLc V (e) log 6 2= cdf (c t jv/ U 6. During radioactive decay beta particles are released. As beta particles pass through wood their speed decreases to % ofthe original speed for every metre ofwood penetrated. Write an equation representing the percent of the original speed of beta particles F after passing through d metres of wood. ç: looj:bf Oe\ 7. Write in exponential form: og626= (: 8. Write as a sum & difference of logs: as a sum: as a difference: _t (6j 2Lf fo 84 (OJ s) [Of J 2_. 9. Write as a single logarithm. log 62O = L Loq 2ot

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