Proving Exponential Growth: Equal Factors over Equal Intervals

The video tutorial explains that exponential functions grow by equal factors over equal intervals. It demonstrates this concept algebraically, showing that the growth factor is independent of specific x-coordinates. The tutorial uses graphs to illustrate exponential growth and provides a detailed proof that equal x-intervals result in equal growth factors. A specific example is used to reinforce the concept, showing how to calculate the growth factor for a given function.

What is the general form of an exponential function?

• y = a - b^x

• y = a / b^x

• y = a * b^x

• y = a + b^x

In the example where x goes from 2 to 4, what is the growth factor?

• 2

• 3

• 4

• 5

What is the growth factor for an interval of length k in an exponential function?

• a^k

• b^k

• k^b

• k^a

In the specific example provided, what is the growth factor when x increases by 5?

• 81

• 125

• 243

• 512

What does the proof demonstrate about exponential functions over equal intervals?

• They grow by equal factors.

• They decrease by equal factors.

• They remain constant.

• They grow by different factors.