The function gives the predicted value of an investment account in dollars, where is the number of years since the account was opened. Which of the following best interprets the factor in this context?
In an exponential model, the number raised to a time variable is the multiplier applied each time the exponent increases by . Read the time unit to tell how often that happens. For a multiplier above , subtract to find the fraction gained. Don’t mistake the whole new amount for the increase.
Hints
- Hint 1
An exponent tells how many times a factor is used. Here counts years. When one year passes, how many more copies of are used? That tells you how often the account changes.
- Hint 2
A multiplier greater than includes the previous balance and something extra. Compare with , which represents all of the previous balance. What fraction is added?
Step-by-step
Read the yearly growth factor
Step 1Find what happens each year
No Desmos needed. The factor’s meaning follows directly from the exponent.
The exponent counts years. Each time increases by , the model uses one more factor of , so the previous balance is multiplied by each year. It isn’t increased by a fixed $1.05.
- Step 2
Convert the factor to an increase
The growth factor includes the whole previous balance, represented by . Subtract to isolate the part added:
Since , the investment account increases by of its previous balance each year. Choice B.