What you’ll learn
Model exponential growth.
Key idea
A growth factor includes the existing whole as well as the added fraction.
The full growth multiplier retains the existing whole before adding the growth fraction.
Worked example
Enter the exact value or ordered values in the format requested below.
A measured quantity P starts at 150 units at t=0, increases 40% of its CURRENT amount after each whole period; t is a nonnegative integer. Write the complete model P in terms of t.
- Growth retains the current whole plus 0.4 more, so multiplier is 1.4.
- P=150(1.4)^t gives 150 at zero periods and 210.0 after one; consecutive values have ratio 1.4.
Answer: P=150(1.4)^t
Quick Check
Choose which candidate representation satisfies the requirements of 'Model exponential growth' and justify the choice.
A measured quantity P starts at 350 units at t=0, increases 5% of its CURRENT amount after each whole period; t is a nonnegative integer. Select with starting-value AND multiplier evidence.