# Thread: Combinations Function word problem

1. ## Combinations Function word problem

Hi,

I hope someone can help me figure out why the range for this word problem:

Note: knowing example 3 isn't necessary.

I have already developed the right equation for this word problem, which is f(x) = 5000 - 25t - 1000cos((pi/6)t). I now just need to determine what the range is. Apparently the range is from 0 to 3850. I personally do not see where the number came from. Can someone please help me?

Sincerely,
Olivia

2. ## Re: Combinations Function word problem

the population cannot be less than zero, so $P(t) \ge 0$

for $t \ge 0$, my graph of $P = 5000-1000\cos\left(\dfrac{\pi t}{6}\right) - 25t$ shows a maximum population of about $5850$ at $t \approx 5.91$ ...

3. ## Re: Combinations Function word problem

Yeah I see that the max range would be 5850. I think my textbook's solution is just wrong. Thanks