00:01
All right, so in this problem, we are told that we are investing $18 ,000 total into a savings that pays 5 % annual interest and then the rest will go into a savings that pays 8 % annual interest.
00:16
So very first question, it says, what are the possible values of x in this situation? so what we want to do first is we want to define what x is representing before we actually get into the numerical values.
00:28
So if i have $18 ,000 total, x is the amount that i'm investing in the 5 % fund.
00:38
So for example, you could potentially invest $10 ,000 of that $18 ,000 into the 5%, which would leave $8 ,000 left for the amount invested into the 8%.
00:50
So basically, x can be anything from zero up to $18 ,000 because that's the total amount of money that you have.
00:57
So if we're saying that in inequality notation, we would say zero is our lower boundary.
01:03
X has got to be greater than or equal to that.
01:05
And it can't go above $18 ,000 because we don't have more than $18 ,000.
01:09
So that would be inequality notation.
01:12
If you're trying to write it in interval notation, we would use brackets to say zero is included.
01:19
That's my lower boundary.
01:20
My upper boundary would be $18 ,000 also with a bracket because that could be included.
01:25
Letter b asks if we're investing x dollars at 5%, write an equation that describes our total interest from both accounts at the end of one year.
01:35
So i just set up a little verbal model here.
01:37
It's my total interest is going to be the interest i earn from 5 % plus the interest i earn from 8%.
01:44
Total interest, we're told, is modeled by the capital letter i.
01:47
So i can start with i is equal to.
01:49
And then 5 % written as a decimal in math is going to be 0 .05.
01:55
If you just write 0 .5, that's actually indicating 50%.
01:58
That's a common mistake there.
02:00
So we're going to get 5 % of the money we put into the 5%, which is denoted by x.
02:09
After that, we want 8 % as a decimal.
02:12
It's going to be 0 .08.
02:14
And then here's how we're going to write the quantity for what we're investing into the 8 % fund.
02:19
It's going to be our total, $18 ,000, that we have minus whatever our x value is there.
02:27
The reason that is is depending on what this x is represented by, maybe it's $10 ,000 or $15 ,000.
02:34
The way that we would figure out this quantity is subtracting x from our total amount that we're investing.
02:39
So for example, if i had $3 ,000 invested for x, and this is just hypothetical, that would leave $18 ,000 minus $3 ,000, or $15 ,000, left to invest the rest into that 8 % fund.
02:58
So that's kind of where we're getting those values from in that equation.
03:03
Now letters c and d ask you to use a graphing utility, so i'm going to use a ti -84 to answer those questions with you.
03:10
So let me switch over to that.
03:14
All right, the very first thing you want to do is go ahead and type in that equation that we found into your y equals.
03:21
So if you hit your y equals at the top left of your calculator, we can type out that same thing that we ended up figuring out for part b.
03:30
Now the problem asks us to graph and trace to estimate how much mary ellen invested at 5 % if she earned $1 ,020 in total interest.
03:38
So the very first thing we want to do is we want to hit that graph button...