Exponential Functions and Growth Factors

The video tutorial explains the exponential function P = 500 * 2^T, identifying it as exponential due to its form y = a^x. The teacher verifies this by creating a table showing how P changes with T, demonstrating that P doubles with each unit increase in T. The video concludes that the function is exponential, as P grows by a factor of two, not a constant amount, which would indicate linear growth.

What is the base of the exponential function P = 500 * 2^T?

• 500

• 2

• T

• P

How can you verify that a function is exponential?

• By checking if it has a constant addition

• By checking if it has a constant multiplication

• By checking if it has a constant division

• By checking if it has a constant subtraction

What is the value of P when T is 0 in the function P = 500 * 2^T?

• 1000

• 500

• 0

• 2000

What happens to the value of P when T increases by 1 in the function P = 500 * 2^T?

• P doubles

• P increases by 500

• P increases by 1000

• P remains the same

Why is the function P = 500 * 2^T not considered linear?

• Because it has a constant addition

• Because it has a constant division

• Because it has a constant multiplication

• Because it has a constant subtraction

What is the growth factor of the function P = 500 * 2^T?

• 500

• 2

• T

• P

If P grows by a factor of two for each unit increase in T, what type of function is it?

• Linear

• Quadratic

• Exponential

• Logarithmic

What would make a function linear instead of exponential?

• Decaying by a constant factor

• Growing by a constant amount

• Growing by a constant factor

• Decaying by a constant amount