# Rational Inequalities

• November 22nd 2009, 01:00 PM
willman32
Rational Inequalities
A biologist predicted that the population of tadpoles in a pond could be modelled by the function f(t)= (40t)/((t^2)+1), where t is given in days. The function that actually models the tadpole population is g(t) = (45t) / ((t^2)+8t + 7).
Determine where g(t) > f(t).

There are a string of these problems.. How would I solve these kinds of questions?
• November 22nd 2009, 01:18 PM
pickslides
Quote:

Originally Posted by willman32
Determine where g(t) > f(t).

I'll get you started

$\frac{45t}{t^2+8t + 7} > \frac{40t}{t^2+1}$

Divide both sides by 5t

$\frac{9}{t^2+8t + 7} > \frac{8}{t^2+1}$

then cross multipling

$9(t^2+1) >8(t^2+8t + 7)$

expanding

$9t^2+9 >8t^2+64t + 56$

and grouping all terms to 1 side

$t^2-64t-47 >0$

now you just need to solve this quadratic.