Understanding Linear and Exponential Functions

This lesson explores predicting future changes using exponential models. It covers compound interest calculations, comparing linear and exponential growth, analyzing profit growth, and understanding depreciation. The lesson emphasizes the difference between constant and increasing rates of change, and how to calculate percent change in various contexts.

What is the formula used to calculate compound interest?

• A = P(1 + r)^t

• A = P(1 - r)^t

• A = P(1 + rt)

• A = P(1 + r/n)^(nt)

If Toby's running time improved from 14.2 seconds to 12.9 seconds, what is the percent change?

• 11%

• 10%

• 8%

• 9%

In a linear function, what remains constant?

• The exponent

• The percent change

• The rate of change

• The base value

How do you determine if a growth pattern is exponential?

• The rate of change increases

• The initial value is zero

• The rate of change decreases

• The rate of change is constant

What is the percent change if a company's profit increases from $1,000 to $1,060?

• 5%

• 6%

• 8%

• 7%

What is the principal amount in the future growth prediction example?

• $1,262

• $1,850

• $1,000

• $1,791

How is depreciation different from exponential growth?

• Depreciation remains constant

• Depreciation is unpredictable

• Depreciation increases over time

• Depreciation decreases over time

What is the percent change in the car depreciation example?

• 7.0%

• 8.0%

• 6.5%

• 7.5%

What happens to the graph of a depreciating asset over time?

• It becomes exponential

• It becomes steeper

• It flattens out

• It remains linear

What is the key takeaway from the lesson on exponential models?

• Exponential models are only applicable to financial scenarios

• Exponential models are unpredictable

• Exponential models have a constant rate of change

• Exponential models can be used to predict future growth and depreciation