Select the correct systems of equations.
2 answers:
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This problem can be solve by graphing (technology), as suggested.
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.
Answer:
The integral for the arc of length is:
By using Simpon’s rule we get: 1.5355453
And using technology we get: 2.3020
The approximation is about 33% smaller than the exact result.
Explanation:
The formula for the length of arc of the function f(x) in the interval [a,b] is:
We need the derivative of the function:
And we need it squared:
Then the integral is:
Now, the Simposn’s rule with n=4 is:
In this problem:
So, the Simposn’s rule formula becomes:
Then simplifying a bit:
Then we just do those computations and we finally get the approximation via Simposn's rule:
While when we do the integral by using technology we get: 2.3020.
The approximation with Simpon’s rule is close but about 33% smaller: