Let f(t) represent the number of new U.S. Hotel openings in the year that is t years since 1990. A possible equation for f is f(t)=-37.36t^2+559.33t-595.31

Find when f(t)=700. What does your result mean in terms of the situation?

Find the t-intercepts of f. What do the t-intercepts mean in terms of the situation.

This is what I have so far...

700= -37.36t^2+559.33t-595.31

Then I subtracted the 700 from the 595.31 which leaves me with this:
-37.36t^2+559.33t+104.69

a=37.36
b=559.33
c=104.69

then I set it up in quadratic formula..but now I am stuck.

2. Originally Posted by getnaphd
Let f(t) represent the number of new U.S. Hotel openings in the year that is t years since 1990. A possible equation for f is f(t)=-37.36t^2+559.33t-595.31

Find when f(t)=700. What does your result mean in terms of the situation?

Find the t-intercepts of f. What do the t-intercepts mean in terms of the situation.

This is what I have so far...

700= -37.36t^2+559.33t-595.31

Then I subtracted the 700 from the 595.31 which leaves me with this:
-37.36t^2+559.33t+104.69

a=37.36
b=559.33
c=104.69

then I set it up in quadratic formula..but now I am stuck.
Just relax and take it step by step. And always check your final answer.

$-37.36t^2 + 559.33t - 595.31 = 700$

$-37.36t^2 + 559.33t - 1295.31 = 0$ <-- Watch the negative signs!

So $a = -37.36, b = 559.33, c = -1295.31$

$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

so
$t = \frac{-559.33 \pm \sqrt{(559.33)^2 - 4(-37.36)(-1295.31)}}{2(-37.36)}$

$t = \frac{-559.33 \pm \sqrt{312850.0498 - 193571.1264}}{-74.72}$

$t = \frac{-559.33 \pm \sqrt{119278.9225}}{-74.72}$

$t = \frac{-559.33 \pm 345.367808}{-74.72}$

So either
$t = \frac{-559.33 + 345.367808}{-74.72} =2.86352$
or
$t = \frac{-559.33 - 345.367808}{-74.72} = 12.1078$

I'll let you decide what the interpretation is.

As far as "t intercepts" are concerned, do you know what an "x intercept" is? Points on a function where it crosses the x axis. Well, t is taking the role of x here, so....

-Dan