1. Suppose that the population of rabbits increases by 1.5 times a month. When the initial population is 100, what is the approximate integer population after a year?
The population after n months is given by 100 x 1.5n
There are 12 months in a year, so n = 12.
Well, isn't that multiplying like rabbits! Let's calculate it step by step.
After 1 month: 100 x 1.5 = 150
After 2 months: 150 x 1.5 = 225
After 3 months: 225 x 1.5 = 337.5 (Approximately 338, because I haven't seen a fraction of a rabbit before)
And so on, until we reach 12 months.
After 12 months, the approximate integer population would be:
100 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5
Now brace yourself for the math circus:
1.5 x 1.5 = 2.25 (Approximately 2 because we can't have a fraction of a rabbit)
2 x 1.5 = 3
2 x 2 = 4
3 x 2 = 6
4 x 2 = 8
6 x 2 = 12
8 x 2 = 16
12 x 2 = 24
16 x 2 = 32
24 x 2 = 48
32 x 2 = 64
48 x 2 = 96
Ta-da! After a year, the approximate integer population would be around 96 rabbits. But remember, this is just an approximation. So don't be surprised if you end up with a few more or a few less hopping critters!
To find the population after a year (12 months), we substitute n = 12 into the formula:
Population = 100 x 1.5^12
Calculating this expression, we find:
Population ≈ 100 x 1.5^12 ≈ 100 x 129.74633789 ≈ 12974 (rounded to the nearest whole number)
Therefore, the approximate integer population after a year is 12,974.
To find the approximate integer population after a year, we need to determine the value of n when 12 months have passed.
The population after 12 months can be calculated using the formula: 100 x 1.5^12.
To find this value using a calculator, follow these steps:
1. Start by raising 1.5 to the power of 12. This can be done by entering "1.5^12" into the calculator.
2. Multiply the result by 100 to find the approximate population after 12 months.
By following these steps, you will find the approximate integer population after a year.