(2p^3 · 2p)^2 HELLO I NEED HELP
1 answer:
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General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace for f(x) in the above inequality to find the domain.
The possible solutions of the above inequality are given by the intervals . We need to pick test point from each possible solution interval and check whether that test point make the inequality
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is
Let's think about the information in the problem. The problem tells us a few key points:
- The number of rabbits grows exponentially
- We start with 20 rabbits (
,
)
- After 6 months (
), we have 100 rabbits (
)
Since we know we are going to be working with an exponential model, we can start with a base exponential model:
is the principal, or starting amount
is the growth/decay rate (in this case, growth)
is the number of months
is the number of rabbits
Based on the information in the problem, we can create two equations:
The first equation tells us that , or that we start with 20 rabbits. Thus, we can change the second equation to:
Now, we don't know , but we want to, so let's solve for it.
Now, the problem is asking us how many rabbits we are going to have after one year (), so let's find that:
After one year, we will have 500 rabbits.