Exponential Functions and Logarithms

The video covers Algebra 2 Chapter 7 review, focusing on graphing functions, exponential growth and decay, function translations, logarithms, and solving equations. It explains how to model population growth, translate functions, and solve equations using logarithms and exponential forms. The video also discusses inverse functions and using calculators for complex calculations.

What is the first step in sketching a graph for a given function?

• Create an X and Y chart to find points

• Plot random points on the graph

• Estimate the shape of the graph

• Draw the axes and label them

How do you convert a percentage to a decimal for exponential growth calculations?

• Divide by 10

• Multiply by 100

• Add 0.1

• Divide by 100

What does multiplying a function by a number less than one indicate?

• A reflection

• A vertical compression

• A horizontal shift

• A vertical stretch

What is the result of e raised to the power of 2.2?

• 8.54

• 10.01

• 9.25

• 7.39

What formula is used for continuously compounded interest?

• A = P(1 + rt)

• A = P(1 + r/n)^(nt)

• A = Pe^(rt)

• A = P(1 - r)^t

How do you express 2^x = 128 in logarithmic form?

• x = log_2(128)

• log_128(2) = x

• x = log_128(2)

• log_2(128) = x

What operation is used to combine logarithms with the same base when adding?

• Subtraction

• Division

• Multiplication

• Addition

What is the first step in expanding a logarithmic expression?

• Simplify exponents

• Factor out coefficients

• Combine terms

• Break apart multiplication

How do you use the change of base formula for log base 4 of 14?

• log(4) / log(14)

• log(14) / log(4)

• log_14(4)

• log_4(14)

What is the first step in solving 4^(7x) = 63 using logarithms?

• Divide both sides by 4

• Take the log of both sides

• Multiply both sides by 7

• Subtract 63 from both sides