Graphing Depreciation: Using Exponential Decay Functions

The video tutorial explains how car value depreciates over time, focusing on Rama's car, which loses 11% of its value immediately and 15% annually for five years. It introduces exponential decay functions, clarifies common misunderstandings about percentage loss, and demonstrates how to calculate and graph depreciation. The tutorial emphasizes understanding exponential functions and constructing a graph to visualize depreciation over time.

What happens to the value of a car as soon as it is driven off the lot?

• It loses 11% of its value.

• It gains 11% in value.

• It remains the same.

• It gains 15% in value.

What is a common misunderstanding about a car's value after it loses 11%?

• The car's value remains unchanged.

• The car gains 11% in value.

• The car is worth 89% of its original price.

• The car is now worth 11% of its original price.

How is the value of a car calculated after the first year of depreciation?

• By adding 15% to the current value.

• By multiplying the current value by 0.85.

• By dividing the current value by 0.85.

• By subtracting 15% from the current value.

What is the decay factor used in calculating the car's depreciation?

• 0.85

• 1.15

• 0.15

• 0.89

What does the graph of an exponential decay function look like?

• A zigzag line that crosses the x-axis multiple times.

• A horizontal line parallel to the x-axis.

• A smooth curve that never intersects the x-axis.

• A straight line that intersects the x-axis.

How can Rama estimate the car's value after 10 years?

• By extending the exponential decay curve on the graph.

• By calculating the average depreciation rate.

• By drawing a straight line on the graph.

• By using a linear function.

What happens to the car's value after the initial five-year period?

• It becomes zero.

• It continues to depreciate at the same rate.

• It starts to increase in value.

• It levels off and changes very little.