number sick est. by n = (170t^2)/(t^2 + 1), t wks aft. start

[sillymoiksta]

The problem is as follows:

The number of students at a large high school who will catch the flu during an outbreak can be estimated by n= 170t^2 / t^2 + 1, where t is the number of weeks from the beginning of the epidemic and n is the number of ill people.
A: Perform the division indicated by 170t^2 / t^2 + 1.
B: Use the formula to estimate how many people will become ill during the first week.

For part A it said the answer in the back of the book was 170 - 170/ t^2 +1. I don't understand how they got that answer though. When I tried to solve it, I tried to divide each side by t first to get 170t / t + 1/t. I was going to attempt synthetic division with this equation but that doesn't seem like the right thing to do. It seems like there should be an easier way to do this. Any help would be deeply appreciated.

 

[stapel]

Do the indicated long division of 170t[sup:dztw005h]2[/sup:dztw005h] + 0t + 0 by t[sup:dztw005h]2[/sup:dztw005h] + 1 (that is, converting the "improper" polynomial fraction into "mixed number" form). :wink:

Eliz.

 

[sillymoiksta]

Re: Division

Thanks for the reply. I don't understand how you use the t^2 + 1 to divide though. For other problems in the assignment it has been as simple as
(8x^4 - 4x^2+ x + 4)/ 2x+ 1. I would just divide the top and bottom by 2 to get a division expression as (4x^4 - 2x^2+ 1/2x + 2) / x + 1/2. Then I would use the constant r of the divisor x - r. r in that case would simply be equal to 2 and I'd use that in my synthetic division.

But t^2 + 1 as a divisor throws me off. Would you have to square root each side to get rid of the squared? I'm confused by this.
Thanks.

 

[stapel]

For other problems in the assignment it has been as simple as....
...and I'd use that in my synthetic division. But t^2 + 1 as a divisor throws me off. Would you have to square root each side to get rid of the squared?

Taking the square root would change the exercise. (Twelve divided by two, the square root of four, is not the same as twelve divided by four. Polynomials are no different.)

Instead of attempting to force a non-linear divisor into a linear-only context (synthetic division), try following the instructions and doing the indicated long polynomial division. That method will work for non-linear divisors.

Eliz.

 

[sillymoiksta]

Re: Division

Thanks that way did work a lot better. And for part B of the problem I substituted in 1 for t in the equation and ended up with the answer that one person will get ill during the first week. I think I did that right but just wondering if you think that is right too.
Thanks for your help!