Thread: Use limits in define function

1. Use limits in define function

Hi .
So the function f(t)= 90e^t/(e^t + 5) models the size of colony of black stilts, where t is the number of yeras.
So i know that the number ob black stilts was a 15 when the program of conservation began.
I need to use limits to determine whether the population will increase without bound and what asymptotes does the function f(t) have .

Thx a lot for any help.

2. This function may have vertical asymptotes at where the denominator is zero.

$\displaystyle e^t+5 =0$. Is there a real solution to this equation?

To check horizontal asymptotes, take the limit of function as x goes to infinity. (normally, we check for limits as x goes to negative infinity too. but in this example, the negative values of t doesn't mean anything, because the graph starts at t=0)

3. So obvieasly the function has or meybe have two horizontal asymptotes. So limits to infinity is 90 and also i think there could be another one which is zero but i'm not so sure. At t=0 f(x) = 90 but on the graph i can see from the left side that curve is going really close to zero. For e^x+5=0 function has not vertical asymptote.

My first question was:

How shall i use limits to determine whether the population will increase without bound. I need to show up working.

4. Originally Posted by Snowboarder
So obvieasly the function has or meybe have two horizontal asymptotes. So limits to infinity is 90 and also i think there could be another one which is zero but i'm not so sure. At t=0 f(x) = 90 but on the graph i can see from the left side that curve is going really close to zero. For e^x+5=0 function has not vertical asymptote.

My first question was:

How shall i use limits to determine whether the population will increase without bound. I need to show up working.
$\displaystyle f(t) = \frac{90 e^t}{e^t + 5} = \frac{90}{1 + 5 e^{-t}} \rightarrow \frac{90}{1 + 0} = 90$.

The population approaches the value of 90 as t --> +oo and so the population does NOT increase without bound.