lenny anf george started with 2 rabbits and each month the number of rabbits doubled since each pair of rabbits produced another pair of rabbits.
what is an eqaution for this situation ?
Lenny and george now have 30 million rabbits. how many month have passed ?
Now = time(0) = 2 = 2^1
time(1) = 4 = 2^2
time(2) = 8 = 2^3
...
time(n) = 2^(n+1)
then 2^(n+1) = 10million
log both sides and use rules of logs
(n+1)log2 = log 10million
n+1 = log 10million/lon2 = 7/log2 = 23.25..
n = 22.25
after 23 months there will be more than 30 million
Let's represent the number of rabbits at the end of each month as a sequence.
At the start, Lenny and George have 2 rabbits. After 1 month, the rabbits double, so they have 2 * 2 = 4 rabbits. After 2 months, the rabbits double again, so they have 4 * 2 = 8 rabbits. This doubling continues each month.
Therefore, the equation for this situation is:
Rabbits = 2^n
where n represents the number of months that have passed.
To find out how many months have passed when there are 30 million rabbits, we can set up the equation as follows:
30,000,000 = 2^n
To solve for n, we can take the logarithm of both sides of the equation:
log(30,000,000) = log(2^n)
Using the logarithmic identity log(a^b) = b * log(a), we get:
log(30,000,000) = n * log(2)
Solving for n:
n = log(30,000,000) / log(2)
Using a calculator, we can compute the value of n, which is approximately 24.25349589.
Therefore, it would take approximately 24 months for Lenny and George to have 30 million rabbits.
To find an equation for this situation, we can define a variable to represent the number of months that have passed. Let's call it "m".
Since the number of rabbits doubles every month, we can set up an equation using exponential growth. Initially, Lenny and George start with 2 rabbits, so the equation would be:
Number of rabbits = 2 * (2^m)
Now, let's solve the second part of the question. We know that Lenny and George now have 30 million rabbits. So we can substitute this value into the equation:
30,000,000 = 2 * (2^m)
To find the number of months that have passed, we need to isolate the variable "m". Let's solve for "m" by simplifying the equation:
Divide both sides of the equation by 2:
15,000,000 = 2^m
Now, take the logarithm (base 2) of both sides of the equation:
log2(15,000,000) = log2(2^m)
Using the property of logarithms that states log(a^b) = b * log(a), we simplify the equation further:
log2(15,000,000) = m
Using a calculator to solve for log2(15,000,000), we find that:
m ≈ 23.13
Therefore, it would take approximately 23.13 months for Lenny and George to have 30 million rabbits. Since we cannot have a fraction of a month, we round up to the nearest whole number.
So, the answer is that approximately 24 months have passed.