Solving Exponential Equations and Inequalities

This video tutorial covers solving exponential equations, modeling with exponential functions, understanding compound interest, and solving exponential inequalities. It begins with an introduction to key vocabulary and concepts, followed by detailed examples and explanations of solving techniques. The tutorial also includes real-world applications, such as modeling population growth and calculating compound interest. Finally, it addresses solving inequalities involving exponential functions, emphasizing the importance of maintaining consistent bases.

What is the property of equality for exponential functions?

• If the bases are the same, the exponents must be equal.

• The exponents must always be positive.

• If the exponents are the same, the bases must be different.

• The bases must always be positive integers.

How can you solve the equation 3^x = 9^4?

• By dividing the exponents.

• By converting 9 to 3 squared and simplifying.

• By subtracting the bases.

• By adding the exponents together.

What is the result of solving the equation 2^(5x) = 2^(4x - 2)?

• x = 1

• x = 0

• x = 2

• x = -2

How do you model population growth using exponential functions?

• By setting up an equation with the initial population as the y-intercept.

• By assuming constant growth each year.

• By using only the final population value.

• By using linear functions.

What is the predicted population of Phoenix in 2013 using the exponential model?

• More than 2,000,000 people

• Exactly 2,000,000 people

• Approximately 1,700,221 people

• Less than 1,000,000 people

How much money will be in the account after 8 years if $4,000 is invested at an annual interest rate of 5.4%, compounded quarterly?

• $12,000.00

• $10,000.00

• $8,000.00

• $6,143.56

What does the compound interest formula calculate?

• The total amount of interest earned per year.

• The interest rate as a percentage.

• The initial amount of money you started with.

• The total amount of money in your account after interest.

If 5^(3-2x) > 1/625, what is the range of x?

• x > 3.5

• x < 3.5

• x <= 3

• x = 3.5

How do you solve the inequality 3^(2x+4) < 1/243?

• x < 3

• x = 3

• x > 3

• x <= 3

What is the base condition for an inequality in exponential functions where the inequality holds as greater?

• The base must be less than 1.

• There is no condition on the base.

• The base must be equal to 1.

• The base must be greater than 1.