Final Answer:
The balance grows by a factor of approximately 3 in 33 years, given that the doubling time of the bank account balance is 11 years.
Step-by-step explanation:
In the context of exponential growth, the doubling time represents the duration required for a quantity to double in value. It indicates the rate at which an amount increases. Using the doubling time as a reference, one can determine the factor by which the quantity grows over a specific period.
Given a doubling time of 11 years, to find the factor by which the balance grows in 33 years, divide the time elapsed by the doubling time: 33 years / 11 years = 3. This result indicates that over the 33-year period, the balance would grow by a factor of 3.
Understanding the concept of doubling time is crucial in estimating exponential growth or decay. It helps in predicting future values based on a known growth rate. In this scenario, knowing that the balance doubles in 11 years allows us to ascertain the factor by which it increases over longer periods, such as 33 years, aiding in financial planning and understanding the potential growth of investments or savings.