The population of rabbits in a particular habitat triples every year. If there are 500 rabbits in 2013, when will there be over 100,000 rabbits?
Year 1--2013--3^0*500 = 500 Rabbits
Year 2--2014--3^1*500 = 1500
Year 3--2015--3^2*500 = 4500
Year n--20xx--3^(n-1)*500 = 100,000
3^(n-1)*500 = 100000
3^(n-1) = 200
(n-1)*Log 3 = Log 200
n-1 = Log 200/Log 3 = 4.82
n = 5.82 or 6 Yrs.
To find out when there will be over 100,000 rabbits, we can use exponential growth formula.
The formula for exponential growth is:
Population = Initial population * Growth rate^Number of years
In this case, the initial population (in 2013) is 500. The growth rate is 3 (since the population triples every year). Let's assume the year we are trying to find is "x".
So, the equation becomes:
100,000 = 500 * 3^(x-2013)
To solve for x, we need to isolate the exponent (x-2013). Let's divide both sides of the equation by 500.
100,000 / 500 = 3^(x-2013)
200 = 3^(x-2013)
Now, let's take the logarithm of both sides of the equation to get rid of the exponent.
log(200) = log(3^(x-2013))
Using the property of logarithms, we can bring down the exponent:
log(200) = (x-2013) * log(3)
Divide both sides of the equation by log(3) to solve for (x-2013):
(x-2013) = log(200) / log(3)
Now, let's calculate (x-2013):
(x-2013) = log(200) / log(3) ≈ 6.246
Adding 2013 to both sides, we can find the year "x":
x ≈ 2013 + 6.246 ≈ 2019.25
Therefore, there will be over 100,000 rabbits in the habitat around the year 2019.25, which means sometime within the first quarter of 2019.