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Thread: Exponential Functions and Equations - Practice Test

  1. #1
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    Unhappy Exponential Functions and Equations - Practice Test

    hellooo, i'm having some trouble completing an exponential functions practice test, please help!!!

    please don't use logarithms as i haven't learnt about them and the unit does not cover them.

    i am attaching a pdf file below, the practice test is on the last two pages! it would be great if you can solve the "extended questions" part ONLY, as this is where i have difficulties.

    if you can't view the file, here is a pasted version of the problems:

    11. According to a Statistics Canada report released in 2010, Saskatoon had the fastest-growing population in Canada,with an annual growth rate of 2.77%.
    a) If the growth rate remained constant, by what factor would the population have been multiplied after 1 year?
    b) What function could be used to model this situation?
    c) What are the domain and range of the function for this situation?
    d) At this rate, approximately how long would it take for Saskatoon’s population to grow by 25%?

    12. The measure of the acidity of a solution is called its pH. The pH of swimming pools needs to be checked regularly. This is done by measuring the concentration of hydrogen ions (H+) in the water. The relationship between the hydrogen ion concentration, H, in moles per litre(mol/L), is H(P) = (1/10)P , where P is the pH.
    a) Sketch the graph of this function.
    b) Water with a pH of less than 7.0 is acidic. What is the hydrogen ion concentration for a pH of 7.0?
    c) Water in a swimming pool should have a pH of between 7.0 and 7.6.What is the equivalent range of hydrogen ion concentration?

    13. Lucas is hoping to take a vacation after he finishes university. To do this, hee stimates he needs $5000. Lucas is able to finish his last year of university with $3500 in an investment that pays8.4% per year, compounded quarterly.How long will Lucas have to wait before he has enough money to take the vacation he wants?

    14. A computer, originally purchased for$3000, depreciates in value according to the function V(t) = 3000 (1/2) t/3 , where V is the value, in dollars, of the computer at any time, t, in years. Approximately how long will it take for the computer to be worth 10% of its purchase price?
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  2. #2
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    Re: Exponential Functions and Equations - Practice Test

    11. According to a Statistics Canada report released in 2010, Saskatoon had the fastest-growing population in Canada,with an annual growth rate of 2.77%.
    a) If the growth rate remained constant, by what factor would the population have been multiplied after 1 year?
    b) What function could be used to model this situation?
    c) What are the domain and range of the function for this situation?
    d) At this rate, approximately how long would it take for Saskatoon’s population to grow by 25%?
    Providing you with the answers is not going to help you learn.
    YOU have to do the work.
    Let's look at Q11:
    a) There are basically 2 ways to increase an amount by a given percentage.
    Consider increasing 100 by 20%.
    (1) You can find 20% of 100 and add it on to 100 .... (20/100 *100)+100 = 20+100=120
    OR
    (2) you can find 120% of 100 ....120/100 * 100 = 1.2*100 = 120

    So what's your answer to (a)?
    Thanks from topsquark
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  3. #3
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    Re: Exponential Functions and Equations - Practice Test

    Quote Originally Posted by vanillabean View Post
    13. Lucas is hoping to take a vacation after he finishes university. To do this, he stimates he needs 5000. Lucas is able to finish his last year of university with 3500 in an investment that pays 8.4% per year, compounded quarterly.How long will Lucas have to wait before he has enough money to take the vacation he wants?
    That one is quite basic...
    p(1 + i)^n = f
    p = 3500
    f = 5000
    i = .084 / 4
    n = ?

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