Usain Bolt ran miles in of an hour. A domestic cat runs miles in 9 4 153 1 3 4 3 8 1 of an hour. Would Usain Bolt or a domestic
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In this question, it is given that
Leanne has a gas card that has $150 on it. She spends $25 a week on gas.
And we have to Write a recursive rule that represents the amount of money she has on her gas card after the first week .
Recursive rule shows the relationship between previous value and the current value .
And here, the recursive rule is
Where a(n-1) is the initial amount which is $150 . And a(n) is the amount after n week .
So for n=1, that is amount in the card after 1 week, we will get
And that's the amount remaining in the card after 1 week .
First, we need to solve the differential equation.
This a separable ODE. We can rewrite it like this:
Now we integrate both sides.
We get:
When we solve for y we get our solution:
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
This a separable ODE. We can rewrite it like this:
Now we integrate both sides.
We get:
When we solve for y we get our solution:
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.