What you’ll learn
Rewrite exponential expressions to reveal growth.
Key idea
Successive growth factors multiply; the annual multiplier is the period multiplier raised to its period count.
Successive growth multiplies period factors; annual multiplier is a power, not a sum or period-count scaling.
Worked example
Enter the exact value or ordered values in the format requested below.
An account begins at 100 dollars and increases 8% every quarter-year. Its model is P=100(1.08)^(4t), t in whole years. Rewrite full model as P=A(b)^t revealing annual multiplier.
- There are 4 quarter-year periods per year, each multiplying the previous quantity by 1.08.
- Group repeated factors: annual base=1.08^4=1.36048896, preserving initial 100; year-one prediction=100×1.36048896=136.04889600.
Answer: P=100(1.36048896)^t
Quick Check
Choose which candidate representation satisfies the requirements of 'Rewrite exponential expressions to reveal growth' and justify the choice.
Account growth is 6% per half-year. Table gives year 0: 150 dollars,year 1: 168.5400 dollars. Select an annual model matching the table and period rule.