What you’ll learn
Distinguish linear and exponential models.
Key idea
Linear continuation has constant differences; exponential continuation has constant ratios.
One matched next value is insufficient; distinguish constant difference from constant ratio across the continuation.
Worked example
Enter the exact value or ordered values in the format requested below.
Quantity P starts at 6 when t=0 and is multiplied by 5 after each whole stage; t is a nonnegative integer. Write its full model.
- Initial output is 6, and every whole stage is multiplied by 5.
- The repeated ratio is 5, giving exponential model P=6(5)^t; its first four outputs are [6, 30, 150, 750].
Answer: P=6(5)^t
Quick Check
Choose which candidate representation satisfies the requirements of 'Distinguish linear and exponential models' and justify the choice.
Quantity P starts at 10 when t=0 and is increased by exactly 2 units after each whole stage; t is a nonnegative integer. Table for t=0,1,2,3 is [10, 12, 14, 16]. Choose with repeated-change evidence.