Logarithmic and Exponential Functions

Mrs. Downey covers Algebra 2 Chapter 7, focusing on exponential and logarithmic functions. The video includes graphing exponential functions, modeling population growth, using graphing calculators, evaluating exponential expressions, and solving both exponential and logarithmic equations. Key concepts such as the change of base formula and properties of logarithms are also discussed.

What is the y-coordinate when x = 0 for the function y = 4 * 3^x?

• 4

• 3

• 1

• 0

If the initial population is 415 and it grows at 19% annually, what is the population after 2 years?

• 488

• 415

• 588

• 615

What is the y-coordinate when x = 1 for the function y = 1/2 * 7^x?

• 14

• 7

• 3.5

• 1/2

Which tool is used to graph the function y = 8 * 2^(x-1) - 4?

• None

• Manual calculation

• Graphing calculator

• T-chart

What is the value of e^2.4 rounded to four decimal places?

• 11.0222

• 11.0242

• 11.0231

• 11.0232

How much will $200 grow to in 10 years at a 3.5% annual interest rate compounded continuously?

• $283.81

• $300.00

• $400.00

• $350.00

Convert 3^4 = 81 into logarithmic form.

• log_3(4) = 81

• log_3(81) = 4

• log_4(81) = 3

• log_81(3) = 4

What is the value of log_4(16)?

• 2

• 1

• 3

• 4

What is the inverse of the function y = 4^x?

• y = log_4(x)

• y = 4^(-x)

• y = x^4

• y = 1/4^x

What is the result of log_b(W^2) + log_b(Y^3)?

• log_b(W^2 * Y^3)

• log_b(W^2 - Y^3)

• log_b(W^2 + Y^3)

• log_b(W^2 / Y^3)