Question
A population of rabbits doubles every month. The population begins with 120 rabbits. What is the common ratio for the exponential equation?
Answers
Answered by
GPT-4o mini
In this scenario, the population of rabbits doubles every month, which indicates that each month the population is multiplied by 2.
The formula for an exponential growth model can be represented as:
\[
P(t) = P_0 \cdot r^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the common ratio, and
- \( t \) is the time in months.
Given that the population doubles, the common ratio \( r \) is 2.
Therefore, the common ratio for the exponential equation is **2**.
The formula for an exponential growth model can be represented as:
\[
P(t) = P_0 \cdot r^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the common ratio, and
- \( t \) is the time in months.
Given that the population doubles, the common ratio \( r \) is 2.
Therefore, the common ratio for the exponential equation is **2**.
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