Linear vs Exponential Functions

The video tutorial explores Kesha's two pay options, illustrating the difference between linear and exponential models. Linear functions are explained through equal differences, while exponential functions are demonstrated using equal factors. Examples of both functions are provided with function tables, highlighting their distinct growth patterns. The tutorial concludes by comparing the two models, emphasizing the rapid growth of exponential functions over linear ones.

What are the two pay options Kesha has?

• Earn $3 on the first day with pay doubling each day

• Earn $3 on the first day with pay tripling each day

• Earn $100 each day plus $5 times the total days worked

• Earn $100 each day plus $3 times the total days worked

What characterizes a linear function?

• Equal differences in equal intervals

• Decreasing factors in equal intervals

• Equal factors in equal intervals

• Increasing differences in equal intervals

In a linear function, what happens to the y-value for every change in x?

• It doubles

• It triples

• It changes by a constant amount

• It remains the same

What is a common misunderstanding about exponential functions?

• The factor must be equal to one

• The factor must be less than zero

• The factor must be a negative number

• The factor can be any number

What is the rule for the function f(x) = 3^x?

• Multiply x by 3

• Subtract 3 from x

• Add 3 to x

• Raise 3 to the power of x

How do exponential functions grow compared to linear functions?

• They grow at a much faster rate

• They grow at a slower rate

• They do not grow

• They grow at the same rate

What is the main difference between linear and exponential growth?

• Linear growth is unpredictable, exponential is constant

• Linear growth uses equal differences, exponential uses equal factors

• Linear growth is rapid, exponential is steady

• Linear growth uses equal factors, exponential uses equal differences

By day ten, how much would Kesha earn with the exponential pay option?

• $300

• $100

• $1,000

• $59,049

What does the practical example of Kesha's pay options demonstrate?

• Linear functions grow faster than exponential functions

• Exponential functions grow rapidly over time

• Both pay options result in the same earnings

• Exponential functions grow at a steady rate

What did you learn in this lesson?

• How to solve quadratic equations

• How to distinguish between linear and exponential models

• How to graph linear equations

• How to calculate interest rates