Determining Percentage Rate of Change

This lesson covers the concept of percent rate of change through exponential models. It begins with a review of compound interest, explaining how to calculate future values using the formula A(t) = P(1 + r)^t. The lesson then contrasts linear functions, which have a constant rate of change, with exponential growth, where the rate increases. A practical example of a company's profit growth is analyzed to determine if it's exponential. Finally, the lesson explores depreciation, showing how it can be modeled exponentially, with a focus on predicting future values. The lesson concludes by reinforcing the understanding of exponential models in financial contexts.

What is the formula used to calculate the amount in a compound interest scenario?

• A = P(1 - r)^t

• A = P + rt

• A = P(1 + r)^t

• A = P(1 + rt)

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

• 10%

• 11%

• 9%

• 8%

In a linear function, what remains constant?

• The rate of change

• The exponent

• The base value

• The percent change

How does the rate of change behave in an exponential growth model?

• It fluctuates randomly

• It decreases over time

• It increases over time

• It remains constant

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

• 5%

• 7%

• 6%

• 8%

What is the predicted value of a car after 10 years if it depreciates at a rate of 7.5% annually?

• $8,277

• $9,000

• $10,000

• $11,000

What is the main difference between predicting growth and predicting depreciation using exponential models?

• Both use subtraction

• Both use addition

• Growth uses subtraction, depreciation uses addition

• Growth uses addition, depreciation uses subtraction