Let's think about the information in the problem. The problem tells us a few key points:
- The number of rabbits grows exponentially
- We start with 20 rabbits (
,
)
- After 6 months (
), we have 100 rabbits (
)
Since we know we are going to be working with an exponential model, we can start with a base exponential model:
is the principal, or starting amount
is the growth/decay rate (in this case, growth)
is the number of months
is the number of rabbits
Based on the information in the problem, we can create two equations:
The first equation tells us that , or that we start with 20 rabbits. Thus, we can change the second equation to:
Now, we don't know , but we want to, so let's solve for it.
Now, the problem is asking us how many rabbits we are going to have after one year (), so let's find that:
After one year, we will have 500 rabbits.