What you’ll learn
Understand exponential functions.
Key idea
Compare several consecutive ratios and differences, not just one change.
Increasing outputs alone do not imply linearity; compare several ratios and differences.
Worked example
Classify examples and non-examples for the concept 'Understand exponential functions'.
Classify y=5*5^x on integer x as exponential or non-exponential with defining evidence.
- Input x appears in the exponent; y at zero is 5.
- Each unit input increment multiplies output by 5; differences 20,100,500 are not constant.
Answer: Exponential — each unit input increase multiplies the output by 5.
Quick Check
Classify examples and non-examples for the concept 'Understand exponential functions'.
Classify y=12*2^x on integer x as exponential or non-exponential with defining evidence.