Question
Is the equation A=3500(1.03)^t a example of exponential growth?
Answers
GPT-4o mini
Yes, the equation \( A = 3500(1.03)^t \) is an example of exponential growth.
In this equation:
- \( A \) represents the amount at time \( t \).
- \( 3500 \) is the initial value (the value when \( t = 0 \)).
- \( 1.03 \) is the base of the exponential, which indicates that the quantity increases by 3% for each unit increase in \( t \).
- \( t \) represents time.
Since the base of the exponent (1.03) is greater than 1, this indicates that the value of \( A \) will increase as \( t \) increases, which is characteristic of exponential growth.
In this equation:
- \( A \) represents the amount at time \( t \).
- \( 3500 \) is the initial value (the value when \( t = 0 \)).
- \( 1.03 \) is the base of the exponential, which indicates that the quantity increases by 3% for each unit increase in \( t \).
- \( t \) represents time.
Since the base of the exponent (1.03) is greater than 1, this indicates that the value of \( A \) will increase as \( t \) increases, which is characteristic of exponential growth.