5.1 Solving Exponential Equations

Multiple Choice

Why is it useful to rewrite numbers as exponents when solving equations and inequalities?

• It makes calculations easier and reveals patterns in equations.

• It always gives a larger number.

• It is only used in geometry.

• It is not useful in mathematics.

Multiple Choice

Which steps are necessary to solve the equation 9^(2x-1) = 3^(6x)?

• Rewrite 9 as 3^2, use power of a power, set exponents equal

• Add 1 to both sides, then divide by 2

• Rewrite 3 as 9^1/2, subtract exponents

• Multiply both sides by 6

Open Ended

How does the property of equality for exponential functions help in solving equations like 2^x = 8^3?

Open Ended

What is the solution to the inequality 16^(2x-3) < 8, and what property allows you to compare the exponents?

Open Ended

Explain how the compound interest formula is used to find the balance in an account after a certain number of years. Use the example provided in the image to support your explanation.

Multiple Choice

Which of the following is the correct formula for calculating compound interest?

• A = P(1 + r/n)^(nt)

• A = P(1 + rt)

• A = P(1 - r/n)^(nt)

• A = P + rt

Multiple Choice

Which of the following values are needed to calculate the final balance in a compound interest account?

• Principal amount, interest rate, number of compounding periods per year, time in years

• Principal amount, only interest rate

• Interest rate, only time in years

• Principal amount, only time in years

Multiple Choice

Which of the following is the correct way to rewrite 81 as an exponent?

• 3^4

• 9^2

• 8^2

• 2^8

Open Ended

Reflect on today's lesson about solving exponential equations and inequalities. What is one concept you found most challenging or interesting, and why?