Suppose there are 100 rabbits on an island and that the rabbit population can triple every half-year.
Write an equation you could use to find the number of rabbits, R, after t, years.
Using your equation, determine the amount of rabbits on the island in year 10.
For the equation I put r=9t but when I did the work for how many rabbits will there be in the population I got 116,226,146,700... please help me, i'm all confused! your help will be very appreciated :)
Oh dear, it seems like you've hopped into a bit of a math conundrum! But worry not, my friend, Clown Bot is here to bring some laughter and clarity to the situation.
To find the number of rabbits, R, after t years, you can use the equation:
R = 100 * (3^t/0.5)
Now, let's calculate the number of rabbits on the island after 10 years. Plug in t=10 into the equation:
R = 100 * (3^10/0.5)
R = 100 * (59049/0.5)
R = 100 * 118098
R = 11,809,800
So, after 10 years, there will be approximately 11,809,800 rabbits on the island.
Remember, though, this calculation assumes that no rabbits leave the island and that there are no other factors affecting the population. In reality, it's quite a hare-raising world out there for rabbits!
To find the equation for the number of rabbits, R, after t years, we need to consider that the rabbit population triples every half-year.
Since there are 100 rabbits initially, we know that after 0.5 years, there will be 100 * 3 rabbits. After 1 year, it will be 100 * 3 * 3, and so on.
Since each year has two half-years, the number of half-year periods (h) in t years is given by h = 2t.
Now, we can write the equation for the number of rabbits, R, after t years:
R = 100 * (3^h)
Plugging in the value of h, we get:
R = 100 * (3^(2t))
Now, let's calculate the number of rabbits on the island after 10 years using this equation:
R = 100 * (3^(2t))
R = 100 * (3^(2*10))
R = 100 * (3^20)
R ≈ 348,678,440,100
Therefore, there would be approximately 348,678,440,100 rabbits on the island after 10 years.