Gr12 Mathematics: Ch 2.5 Exponential Functions

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?

pH = -log[H+] Signup and view all the answers

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

x ∈ ℝ Signup and view all the answers

What is the application of logarithms in chemistry?

pH levels Signup and view all the answers

What is the definition of an exponent?

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

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

The graph rises rapidly. Signup and view all the answers

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

y = log_b x Signup and view all the answers

What is the definition of a logarithm?

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

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

Interchange x and y, then solve for y. Signup and view all the answers

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

Increasing. Signup and view all the answers

What is the value of log_a 1?

0 Signup and view all the answers

What is the value of log_a a?

1 Signup and view all the answers

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

2logₐx Signup and view all the answers

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

x = 0 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?

15 years Signup and view all the answers

What is the value of log₁₀(1000)?

3 Signup and view all the answers

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

y > 0 Signup and view all the answers

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

logₐx + logₐy Signup and view all the answers

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

y > 0 Signup and view all the answers

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

y = 0 Signup and view all the answers

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

(1, 0) Signup and view all the answers

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

x = 0 Signup and view all the answers

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

The function is increasing. Signup and view all the answers

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

Zero property Signup and view all the answers

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

Identity property Signup and view all the answers

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

x > 0 Signup and view all the answers

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

n logₐx 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?

Exponential decay Signup and view all the answers

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

1 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?

25 years Signup and view all the answers

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

logₐx + logₐy Signup and view all the answers

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

logₐx - logₐy Signup and view all the answers

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

All positive real numbers 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?

They are inverse functions Signup and view all the answers

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