A population of ladybugs rapidly multiplies so that the population t days from now is given by A(t) = 3000e^(.01t). How many ladybugs are present now? How many will there be after a week?
im totally lost on this one! Where do i begin and where do i end?!
t is the number of days from now. The first question is asking for how many ladybugs are present now. How many days are there from now to well now ;/. So t = ?. How many days are in a week from now?
If it is still not clear, A(t) is the population at any given day and the given day is represented by t. So by substituting a number for t into the function, A(t) = 3000e^(.01t), it will give you the population at the number of days from now. Err, badly phrased it seems but I tried to simplify it as much as possible.
To find the number of ladybugs present now, you can substitute t = 0 into the equation A(t) = 3000e^(.01t). This will give you:
A(0) = 3000e^(.01(0)) = 3000e^(0) = 3000(1) = 3000
Therefore, there are 3000 ladybugs present now.
To find the number of ladybugs after a week, you need to substitute t = 7 into the equation A(t) = 3000e^(.01t). This will give you:
A(7) = 3000e^(.01(7)) = 3000e^(.07)
To evaluate e^(.07), you can use a scientific calculator or an online calculator. In this case, e^(.07) is approximately 1.0724. Hence,
A(7) ≈ 3000(1.0724) ≈ 3,217.2
Therefore, there will be approximately 3,217.2 ladybugs after a week.
In summary:
- The number of ladybugs present now is 3000.
- The number of ladybugs after a week is approximately 3,217.2.