Key Features of Exponential Functions

The video tutorial covers key features of exponential functions, including growth and decay. It begins with an introduction to exponential equations and their components, such as initial value and growth/decay rate. The first example demonstrates exponential growth with f(x) = 2^x, highlighting domain, range, and asymptotes. The second example focuses on graph transformations of f(x) = 3^x, including reflections and shifts. The third example models population growth using exponential equations, while the fourth example explains car depreciation through exponential decay. Each section provides detailed explanations and calculations to illustrate these concepts.

What is the general form of an exponential function?

• a + b^x

• a / b^x

• a * b^x

• a - b^x

What does the parameter 'a' represent in an exponential function?

• Growth rate

• Decay rate

• Initial value

• Horizontal asymptote

As x approaches negative infinity in an exponential growth function, what does y approach?

• One

• Negative infinity

• Zero

• Infinity

What transformation occurs when an exponential function is multiplied by a negative outside the function?

• Reflection over the y-axis

• Reflection over the x-axis

• Shift to the left

• Shift to the right

What is the effect of subtracting a number outside an exponential function?

• Horizontal shift right

• Vertical shift up

• Vertical shift down

• Horizontal shift left

How is the growth factor calculated for a population growing at a rate of 1.3% annually?

• 0.013

• 1.013

• 0.13

• 1.13

If a population of 4.6 million grows at 1.3% per year, what will it be in 30 years?

• 7.78 million

• 6.78 million

• 8.78 million

• 5.78 million

What does a 'b' value less than 1 in an exponential function indicate?

• Oscillation

• Exponential decay

• Exponential growth

• No change

What is the rate of decay if the 'b' value is 0.8?

• 10%

• 15%

• 20%

• 25%

What is the new value of a car after one year if it depreciates at 20% per year from an initial value of $24,000?

• $18,000

• $19,000

• $20,000

• $19,200