Gr12 Mathematics: Ch 2.5 Exponential Functions
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Questions and Answers

What is the logarithmic rule for logarithmic functions?

  • Quotient Rule
  • Power Rule
  • Product Rule
  • Change of Base (correct)

    • What is the graph of the inverse function about?

  • x-axis
  • y-axis
  • origin
  • the line y = x (correct)

    • What is the formula to calculate the population growth?

  • A = P(1 + i)^n (correct)
  • A = P(1 / i)^n
  • A = P(1 * i)^n
  • A = P(1 - i)^n

    • What is the formula to calculate the pH level?

    <p>pH = -log[H+]</p> Signup and view all the answers

    What is the domain of the exponential function f(x) = 10^x?

    <p>x ∈ ℝ</p> Signup and view all the answers

    What is the application of logarithms in chemistry?

    <p>pH levels</p> Signup and view all the answers

    What is the definition of an exponent?

    <p>The number of times a base number is multiplied by itself.</p> Signup and view all the answers

    What happens to the graph of the exponential function f(x) = b^x when b > 1?

    <p>The graph rises rapidly.</p> Signup and view all the answers

    What is the inverse of the function y = b^x?

    <p>y = log_b x</p> Signup and view all the answers

    What is the definition of a logarithm?

    <p>The exponent to which a base must be raised to yield x.</p> Signup and view all the answers

    How do you convert an exponential equation to a logarithmic equation?

    <p>Interchange x and y, then solve for y.</p> Signup and view all the answers

    What is the shape of the graph of the logarithmic function y = log_b x?

    <p>Increasing.</p> Signup and view all the answers

    What is the value of log_a 1?

    <p>0</p> Signup and view all the answers

    What is the value of log_a a?

    <p>1</p> Signup and view all the answers

    If logₐx = 2, what is the value of logₐ(x²)?

    <p>2logₐx</p> Signup and view all the answers

    What is the asymptote of the graph of the logarithmic function f(x) = logx?

    <p>x = 0</p> Signup and view all the answers

    A population grows by 10% every year. If the current population is 10000, how many years will it take for the population to triple?

    <p>15 years</p> Signup and view all the answers

    What is the value of log₁₀(1000)?

    <p>3</p> Signup and view all the answers

    What is the range of the exponential function f(x) = 10^x?

    <p>y &gt; 0</p> Signup and view all the answers

    If logₐx = 2 and logₐy = 3, what is the value of logₐ(xy)?

    <p>logₐx + logₐy</p> Signup and view all the answers

    What is the range of the exponential function y = b^x?

    <p>y &gt; 0</p> Signup and view all the answers

    What is the horizontal asymptote of the exponential function y = b^x?

    <p>y = 0</p> Signup and view all the answers

    What is the intercept of the logarithmic function y = log_b x?

    <p>(1, 0)</p> Signup and view all the answers

    What is the vertical asymptote of the logarithmic function y = log_b x?

    <p>x = 0</p> Signup and view all the answers

    Which of the following is true for the exponential function y = b^x when b > 1?

    <p>The function is increasing.</p> Signup and view all the answers

    What is the property of the logarithmic function y = log_b x that states log_a 1 = 0?

    <p>Zero property</p> Signup and view all the answers

    What is the property of the logarithmic function y = log_b x that states log_a a = 1?

    <p>Identity property</p> Signup and view all the answers

    What is the domain of the logarithmic function y = log_b x?

    <p>x &gt; 0</p> Signup and view all the answers

    What is the value of logₐ(xⁿ) in terms of logₐx?

    <p>n logₐx</p> Signup and view all the answers

    If a radioactive substance decays at a rate proportional to its current mass, which model best represents this decay?

    <p>Exponential decay</p> Signup and view all the answers

    What is the value of logₐ(a) in terms of a?

    <p>1</p> Signup and view all the answers

    A city's population is currently 5000 and grows at a rate of 5% per year. How many years will it take for the population to reach 20000?

    <p>25 years</p> Signup and view all the answers

    What is the value of logₐ(xy) in terms of logₐx and logₐy?

    <p>logₐx + logₐy</p> Signup and view all the answers

    What is the value of logₐ(x/y) in terms of logₐx and logₐy?

    <p>logₐx - logₐy</p> Signup and view all the answers

    What is the range of the function y = b^x when b > 1?

    <p>All positive real numbers</p> Signup and view all the answers

    What is the relationship between the exponential function y = b^x and the logarithmic function y = log_b x?

    <p>They are inverse functions</p> Signup and view all the answers

    If x = b^y, then what is the value of y?

    <p>y = log_b x</p> Signup and view all the answers

    What is the shape of the graph of the exponential function y = b^x when 0 < b < 1?

    <p>Decreasing</p> Signup and view all the answers

    If y = log_b x, then what is the equivalent exponential equation?

    <p>b^y = x</p> Signup and view all the answers

    What is the asymptote of the graph of the exponential function y = b^x when b > 1?

    <p>Horizontal asymptote at y = 0</p> Signup and view all the answers

    If log_b x = 2 and log_b y = 3, what is the value of log_b (x/y)?

    <p>-1</p> Signup and view all the answers

    What is the intercept of the exponential function y = b^x when b > 1?

    <p>(0, 1)</p> Signup and view all the answers

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