Rabbit populations can double (increase by $100\%$) every 30 days. If there are 10 rabbits on a farm, how many rabbits will be on the farm after 120 days?
Future Amount = [?](1 + [])
Answer (1)
Calculate the number of doubling periods: 30 120 = 4 .
Use the formula for exponential growth: Future Population = Initial Population × 2 Number of Doubling Periods .
Substitute the given values: Future Population = 10 × 2 4 .
Calculate the future population: 10 × 16 = 160 .
Explanation
Understanding the Problem We are given that a rabbit population doubles every 30 days. We start with 10 rabbits and want to know how many rabbits there will be after 120 days.
Calculating the Number of Doubling Periods First, we need to determine how many 30-day periods there are in 120 days. To do this, we divide the total time (120 days) by the doubling time (30 days): 30 days/period 120 days = 4 periods So, the rabbit population will double 4 times.
Calculating the Future Population Now, we can calculate the future rabbit population using the formula for exponential growth. The formula is:
Future Population = Initial Population × 2 Number of Doubling Periods
In this case, the initial population is 10 rabbits, and the number of doubling periods is 4. So, we have:
Future Population = 10 × 2 4
Since 2 4 = 16 , we get:
Future Population = 10 × 16 = 160
Therefore, after 120 days, there will be 160 rabbits on the farm.
Final Answer After 120 days, there will be 160 rabbits on the farm.
Examples
Exponential growth, like the growth of the rabbit population in this problem, can be applied to many real-world scenarios. For example, it can model the growth of bacteria in a culture, the accumulation of money in a savings account with compound interest, or the spread of a virus in a population. Understanding exponential growth helps us make predictions and informed decisions in various fields, from biology and finance to public health.
