Exponential Functions and Their Applications

This video tutorial by Deni Handayani on the Net Lab channel covers the second part of the topic on exponents and logarithms, focusing on exponential functions. It explains the definition, general form, and graphing of exponential functions, and provides examples to illustrate these concepts. The video also discusses the application of exponential functions in real-world scenarios, such as growth and decay processes. Additionally, it includes practice problems to reinforce understanding and offers information on joining an online learning platform for further study.

What is the general form of an exponential function?

• f(x) = ax + b

• f(x) = a^x + b^x

• f(x) = k * a^x

• f(x) = x^2 + bx + c

Which of the following is NOT a condition for the base of an exponential function?

• The base must be greater than zero.

• The base can be equal to one.

• The base must be positive.

• The base cannot be negative.

Which of the following is an example of an exponential function?

• f(x) = 3^x

• f(x) = x^3

• f(x) = 3x + 2

• f(x) = x/3

What happens to the graph of an exponential function when the base is greater than one?

• It decreases as x increases.

• It forms a parabola.

• It remains constant.

• It increases as x increases.

If the base of an exponential function is between 0 and 1, what is the behavior of its graph?

• The graph decreases as x increases.

• The graph forms a circle.

• The graph increases as x increases.

• The graph is a straight line.

Which point is NOT on the graph of y = 2^x - 3?

• (2, 0)

• (1, -1)

• (0, -2)

• (2, 1)

What is the y-intercept of the function y = 2^x + 2?

• (0, 3)

• (0, 5)

• (0, 2)

• (0, 4)

In the context of exponential growth, which of the following scenarios is an example?

• Erosion of a mountain

• Cooling of a hot object

• Population growth of a city

• Decay of a radioactive substance

What is the initial mass of a radioactive substance if its decay is modeled by y = 10 * (1/2)^(t/25)?

• 10 grams

• 20 grams

• 15 grams

• 5 grams

After 100 years, what is the mass of a radioactive substance modeled by y = 10 * (1/2)^(t/25)?

• 0.625 grams

• 5 grams

• 1.25 grams

• 2.5 grams