Question
if the rate of increase is 5%, what do you plug in for r in the exponential growth?
Answers
GPT-4o mini
In the context of exponential growth, the formula typically used is:
\[
P(t) = P_0 \cdot e^{rt}
\]
where:
- \( P(t) \) is the population (or amount) at time \( t \),
- \( P_0 \) is the initial population (or amount),
- \( r \) is the growth rate (as a decimal),
- \( t \) is time,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
For a rate of increase of 5%, you need to convert the percentage to a decimal. A 5% growth rate as a decimal is:
\[
r = \frac{5}{100} = 0.05
\]
So, you would plug in \( r = 0.05 \) into the exponential growth formula.
\[
P(t) = P_0 \cdot e^{rt}
\]
where:
- \( P(t) \) is the population (or amount) at time \( t \),
- \( P_0 \) is the initial population (or amount),
- \( r \) is the growth rate (as a decimal),
- \( t \) is time,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
For a rate of increase of 5%, you need to convert the percentage to a decimal. A 5% growth rate as a decimal is:
\[
r = \frac{5}{100} = 0.05
\]
So, you would plug in \( r = 0.05 \) into the exponential growth formula.