Question

f(t)= 1+.9e^(-.02t) with t ≥ 0
find the limit as t approaches infinity of f(t)

Answer 1

Have you already filled in +infinity?

Answer 2

Do you understand what happens to a graph when an exponent is negative?

Answer 3

no? haha sorry what happens?

Answer 4

okay, when an exponent is negative, and you fill in very big numbers, this 'part' of the equation will become zero

Answer 5

You have yourself two parts:
1
and
.9e^(-0.2t)

Answer 6

so the .9e^(-.02t) part becomes zero? I'm not really sure what you mean

Answer 7

Yes, that is correct, but let me rewrite it! Then it will become clear to you too!!

Answer 8

I will give you an example:
\[2^{-2}=\frac{ 1 }{ 2^{2} }=\frac{ 1 }{ 4 }\]

Answer 9

Do you understand this?

Answer 10

yes i see that

Answer 11

okay, Now fill in an infinity, you will have instead of -2, -infinity

Answer 12

So then again, apply the 'fraction-rule'

Answer 13

You will see that when you divide e ( or whatever number) by infinity, you will end up having zero

Answer 14

so:
\[e^{-infinity}=\frac{ e }{ infinity }\rightarrow0\]

Answer 15

And since the other part of your equation (in your question) is a constant (=1), you'll end up with 1 as an answer, because this doesn't include a variable...so this number just stays 1

Answer 16

so the limit is 1?

Answer 17

yes

Answer 18

But the most important thing is the reformulation of e^(-infinity) = 1/(infinity) = 0 !!

Answer 19

always try to fill in numbers like -infinity, 0, 1, and +infinity.
It really helps you to 'see' or understand what happens to a graph

Answer 20

For example: put in -infinity, do you understand what happens?

Answer 21

\[e^{-(-infinity)}=e^{+infinity}=infinity\] So your graph will rise skyhigh towards infinity (for -infinity, so you go to the left of your graph)

Answer 22

in your question I mean in this example

Answer 23

okay i see what you're saying... and because it's negative that means that the entire function is decreasing right?

Answer 24

yes! (ofcourse: THAT PART of the equation)

Answer 25

The 1 still remains 1, because that part doesn't include a variable t

Answer 26

Good luck

Answer 27

thank you!!