[MOVED] ((t^3 - 4t^2 - 5t)a) / (22t^2 - 110t) for t=5, a=200

[Jaspworld]

A formula for calculating the drug dose for young children is ((t^3 - 4t^2 - 5t)a) / (22t^2 - 110t), where t is the age of the child in years and a is adult dose. If the adult dose for a certain antibiotic is 200 mg, what dose does the formula indicate for a 5-year old child.

This is how I solved the question. First of all I found the restrictions, which were 0 and 5. Then I simplified the formula. However, after I simplified the formula I was able to substitute 5 into the formula. But since 5 is a restriction on the formula, I can't solve for t=5. So, my answer was that since 5 is a restriction on the formula, it can't be solved for. However, in the back of the book, they have an answer, which is obtained by substituting 5 for a in the simplified formula.

Can you clarify which one is correct? Thanks.

 

[Deleted member 4993]

Re: Please Clarify!

A formula for calculating the drug dose for young children is ((t^3 - 4t^2 - 5t)a) / (22t^2 - 110t), where t is the age of the child in years and a is adult dose. If the adult dose for a certain antibiotic is 200 mg, what dose does the formula indicate for a 5-year old child.

This is how I solved the question. First of all I found the restrictions, which were 0 and 5. Then I simplified the formula. However, after I simplified the formula I was able to substitute 5 into the formula. But since 5 is a restriction on the formula, I can't solve for t=5. So, my answer was that since 5 is a restriction on the formula, it can't be solved for. However, in the back of the book, they have an answer, which is obtained by substituting 5 for a in the simplified formula.

Can you clarify which one is correct? Thanks.

D(t) = ((t^3 - 4t^2 - 5t)a) / (22t^2 - 110t)

= {at(t^2 - 4t - 5t)} / {22t(t - 5)}

= {at(t - 5)(t + 1)} / {22t(t - 5)}

You have "removable discontinuity" at t=0 and t = 5 - since t and (t-5) can be factored out. In your graphical calculator - graph the function - and study it.

D(t) = {a(t + 1)} / {22}

Now you can evaluate the function at t = 5

incidentally -

d(21) = a <------------that makes sense.