Exponential and Geometric Functions

This video tutorial prepares students for a quiz on geometric sequences and exponential functions. It covers the explicit rule for geometric sequences, simplifying negative exponents, evaluating functions, and calculating specific terms in sequences. The tutorial also includes practical examples like determining the height of a ball after bounces and identifying sequence types. Additionally, it explains how to graph exponential functions and analyze their properties.

What is the main focus of the upcoming quiz in the Integrated Math class?

• Statistics and probability

• Quadratic equations and functions

• Geometric sequences and exponential functions

• Linear equations and inequalities

What is the explicit rule for a geometric sequence?

• a_n = a_1 + (n-1)d

• a_n = a_1 / r^(n-1)

• a_n = a_1 * n^r

• a_n = a_1 * r^(n-1)

If the second term of a geometric sequence is 5 and the third term is 10, what is the common ratio?

• 5

• 2

• 10

• 1

How do you simplify an expression with a negative exponent?

• Subtract the exponent from the base

• Flip the base to the denominator and make the exponent positive

• Add the exponent to the base

• Multiply the base by the exponent

What is the result of evaluating f(x) = -2^x for x = 4?

• 16

• 8

• -8

• -16

What is the 10th term of a geometric sequence with a first term of 127 and a common ratio of 3?

• 59049

• 729

• 2187

• 19683

In the bouncing ball problem, what is the height of the third bounce if the initial height is 18 feet and the bounce ratio is 0.75?

• 5 feet

• 6 feet

• 7 feet

• 8 feet

Which of the following sequences is geometric?

• 1, 4, 7, 10

• 2, 4, 8, 16

• 3, 6, 9, 12

• 5, 10, 15, 20

Do the functions f(x) = -2 * 3^x and g(x) = -2 * 0.5^x have the same y-intercept?

• Yes

• No

• Only f(x) has a y-intercept

• Only g(x) has a y-intercept

What is the end behavior of the function y = -2/3 * 5^x as x approaches positive infinity?

• The function approaches negative infinity

• The function approaches positive infinity

• The function remains constant

• The function approaches zero