Geometric and Exponential Functions

The video covers exponential relationships in math, focusing on solving and graphing exponential functions. It explains geometric sequences, their formulas, and real-world applications, such as population growth and financial calculations. The teacher provides examples and step-by-step solutions, emphasizing the importance of understanding the rate of change and the behavior of exponential graphs.

What does it mean for a variable to be in the exponent part of an equation?

• The variable is added to the base.

• The variable is subtracted from the base.

• The variable is multiplied by the base.

• The variable is the power to which the base is raised.

How do you isolate the variable in an exponential function?

• Subtract the base from both sides.

• Add the base to both sides.

• Multiply both sides by the base.

• Divide both sides by the base.

What happens to a number with a negative exponent?

• It becomes zero.

• It becomes a positive exponent in the denominator.

• It becomes a negative exponent in the numerator.

• It remains the same.

What is the rate of change in a geometric sequence?

• The difference between terms.

• The ratio between consecutive terms.

• The sum of the terms.

• The product of the terms.

How do you write an explicit rule for a geometric sequence?

• Using the product of all terms.

• Using the difference between the first two terms.

• Using the first term and the common ratio.

• Using the sum of the first and last terms.

What is the formula for the nth term of a geometric sequence?

• First term plus common ratio times n.

• First term times common ratio to the power of n-1.

• First term divided by common ratio to the power of n.

• First term minus common ratio times n.

How do you find the next term in a geometric sequence?

• Subtract the common ratio from the last term.

• Multiply the last term by the common ratio.

• Add the common ratio to the last term.

• Divide the last term by the common ratio.

What is the shape of the graph of an exponential function?

• A straight line.

• A parabola.

• A J-curve.

• A circle.

What does the base of an exponential function represent in population growth models?

• The time period.

• The growth rate.

• The initial population.

• The final population.

How do you determine if a sequence is geometric?

• Check if the product of terms is constant.

• Check if the sum of terms is constant.

• Check if the ratio between terms is constant.

• Check if the difference between terms is constant.