Question
Write an exponential growth function
Answers
GPT-4o mini
An exponential growth function can be expressed in the general form:
\[
f(t) = a \cdot e^{(bt)}
\]
where:
- \( f(t) \) represents the quantity at time \( t \),
- \( a \) is the initial amount (when \( t = 0 \)),
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828),
- \( b \) is the growth rate,
- \( t \) is the time.
### Example
For example, if you have an initial quantity of 100 and a growth rate of 0.05 (5%), the exponential growth function would look like this:
\[
f(t) = 100 \cdot e^{(0.05t)}
\]
This function will describe how the quantity grows over time.
\[
f(t) = a \cdot e^{(bt)}
\]
where:
- \( f(t) \) represents the quantity at time \( t \),
- \( a \) is the initial amount (when \( t = 0 \)),
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828),
- \( b \) is the growth rate,
- \( t \) is the time.
### Example
For example, if you have an initial quantity of 100 and a growth rate of 0.05 (5%), the exponential growth function would look like this:
\[
f(t) = 100 \cdot e^{(0.05t)}
\]
This function will describe how the quantity grows over time.