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exponential growth problem? i don't get it!?
The population of rabbits on an island is growing exponentially. In 1960 there were 400 rabbits and by 1970 this population had grown to 2400 rabbits. Thus the population of rabbits t years after 1960 is given by
R(t)= R * 2^(t/K)
it wants me to find t. i did and its 400.
how would i go about finding K? is that the same as the doubling time? please help!
1 Answer
- Anonymous1 decade ago
First step is to setup the equation. This is probably the most important part of this problem, because setting up the equation properly is the only way to have a chance at finding the answer.
R(t) = R(0) * 2^(t/K)
You know the following:
R(0) = 400, where t=0 in 1960
R(10) = 2400, since t=10 in 1970
Then if you setup the equation at t=10,
R(10) = R(0) * 2^(10/K)
2400 = 400 * 2^(10/K)
If you understand the above, then you are halfway there!
Now you have enough information to solve for K. You can use algebra and log rules.
2400/400 = 2^(10/K)
6 = 2^(10/K)
log 6 = log (2^(10/K)) //take log of both sides to get rid of the ^
log 6/log 2 = 10/K //if needed ask your parents or a math
//teacher about this step
.778/.301 = 10/K //use a calculator to figure out the logs
2.585 = 10/K
K = 10/2.585
K = 3.8685