For Mathguru

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Math 30-1: Unit 3/4 Exponents and Logs Assignment

Name: _____________________________

If your name does not appear in your writing on the hardcopy scan – you will lose one mark!

For all questions, show work and clearly indicate your final answer.

1. State the exponential function represented by the graph. (1 mark)

2. Write the equation for each of the following transformations to the function y = 4x. Then, state

the domain and range of the transformed function. (2 marks)

“horizontally stretched by a factor of 2, translated 3 units right and 1 unit down”

3. Solve each of the following equations algebraically. (8 marks)

a) b)

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4. Write each expression in logarithmic form. (2 marks)

5. Write each expression in exponential form. (2 marks)

6. Identify the transformations in .State the domain, range, and

intercepts of the graph. Round your answers to one decimal place if necessary. (3 marks)

7. Write the equation for each of the following transformations to the function y = log x. Then,

state the domain and range of the transformed function. (2 marks)

“ translation 5 units right and 4 units down”.

8. Use the laws of logarithms to evaluate each of the following. (4 marks)

9. Write each of the following as a single logarithm. (4 marks)

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10. (2 marks)

11. Solve the following logarithmic equations algebraically. (12 marks)

12. Solve the following exponential equations algebraically using logarithms. Round your

answers to the nearest hundredth. (4 marks)

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13. The intensity of sound is measured in decibels (dB). The level of a sound, L, is given by

where I is the intensity of the sound and I0 is the faintest sound detectable to humans. A

sound engineer increases the volume at a concert from 90 decibels (dB) to 93 dB. Show that

this increase approximately doubles the intensity of the sound. (2 marks)

14. A strain of bacteria doubles every 4 hours. A sample contains 40 bacteria. Determine the

time needed until 1000 bacteria are present. (Show work-including the equation developed

and round your answer to two decimal places.) (2 marks)

15. A water filter removes 40% of the impurities in a sample of water. Write an exponential

equation to determine the percent of impurities remaining, P, after the water has passed

through n filters. Then determine how many filters are needed to remove at least 99% of

impurities in the water. SHOW ALL WORK. (3 marks)