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Yeueaidcbr 01 $900 Dy paring 2346remairng btlancemonuluunulemalaing Gebt months...

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Yeueaidcbr 01 $900 Dy paring 2346remairng btlancemonuluunulemalaing Gebt months

Yeueai dcbr 01 $900 Dy paring 2346 remairng btlance monu luunul emalaing Gebt months



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Solve the following problems by showing your complete solution. Accumulate $\mathrm{P} 12,000$ at $3 \frac{1}{2}$ $\%$ simple interest for 9 months.

So high. So this is a problem with 30. And very similar problem that we did earlier. So the question says that social has a community for time deposit account of repeat 800 per month at 6% per annum. And if he gets a piece 1300 as interested in finding a little time for which the count was held in months. So here we are quite to find the time in months. So you know the forms of simple interest which is okay which is the monthly amount is depositing into end into endless one divide by two which is any number of months into 1/12 into Questioned Ages eight which is out over 100. So we know how much uh Interest he has received. She has received airbase 1300 as interest. So yeah And how and she's playing with 800 per month. gave 800 into an and we need to finance. So I simply go and expand it and square this end over to Yeah every year. And the question did impressions 6%. So if I uh feeling this function up. Yeah. Yeah. 800 in the house. Yes. Yeah into 1/12 Into six. Over 100. I don't care Gives me too. So it's 1300. Okay to. Yeah and describe less in. If I divide two on both sides I will have 750 here and an inscribed let's in if you. Mhm. And an inscribed this and -750 simply I need to mediate uh bring them right to just and a square plus 26 and -25 and minus 7 15. Taking the end common I get n less 26 And taking 25 common here uh negative 25 common here. I will have N last 26 year again. So in -25 and N last 26 Equals zero and it's 25 and And it's -26. So we know a number of months can be can already didn't zero. Therefore the right answer here is and 25 which is option number two of the possibility of cancers. So I hope the expansion was helpful and clear. Thank you for your time.

If given the context 51 $1000 in 12 months and were asked to write this as a unit rate, so you never rate. First, let's write it just at a rate so 51,000 over 12 months and I want to get this unit to the one. So nor did you do that. I need to divide by 12 right? Which means that all soft divide my $51,000 by 12. So 51,000 divided by 12 is 4250 her month. So one month and we don't have to write the one there. It's understood that this is 4000 to 50 per month, and this is Theo unit rate.

And this exercise, we're being given a table of data. The input is years from 1998, and two years increments. The output is the value of 3247: 5836. And we're being asked to find a model equation that would fit that data in quadratic form using translations, A H and K. Right? I have a graft all of that data here in Desmond's that we can look at it. I can see that it starts here at 1997. I'm sorry. at 1998 with the value of 3247 between 3000 and 3500 and the rate of increase gradually gets faster so that it looks like the values are getting higher more quickly. It's curving up, it looks like it might be a good candidate for a quadratic model. We could just start by using this initial point 1998 as the vertex of that. For Avalon I'm going to do that. That means that my starting year is shifting from 0 to 1998 to change that starting point and subtracting 1998 from the input and then To get the Vertex all the way up to 3247. I need to add that. That was my K value. If my stretch factor is just one, if it's a regular shape, I can see that. Yes, the problem goes through that. That's a fact vertex. It's very shallow right now because this scale is going in increments of 500. Every measure Interval, every major grid line represents 500. So it's being compressed a lot by the scale over the graph. My next task is to figure out what is the stretch factor A. That will make that problem fit the rest of data. So let's switch over to this whiteboard. I have already said that I am using the first point for my H and K values to get that vertex. So I'm going to rewrite my equation with this 0.0.1998 and 3247 ordered pair plugged in as my hk I'm shifting my starting year 1998. Yeah mm I am shifting my starting value up to 3247 247 So that's the beginning of my equation. Let me a great that seven. Better. I need to find this stretch factor. What I'm going to do is use another point of data. I've got this 0.0.2006 gives me 5,836 as an output. Yeah, That point has to be part of this equation. So if I put that X. Value 2006 in I need to get that 5,836 out. And that means I have to have an a value a stretch value that will make that work. So I'm going to do exactly that. I'm going to plug that point in with the input in the X. And the output in the UAE and then I'm going to solve to find out what a value makes that true so. Mhm. My y value is going to be 5836 if I have the right stretch factor. Mhm. When my input is 2006. Okay from this parable that's been shifted To a new starting year of 1998 and shifted up to give me a starting value Of 3247. Yeah. Mhm. Now I've got the equation I can solve for a, I'm going to start with parentheses. E. Is figure out what this is. So 5836 equals whatever my stretch value is, my stretch factor, 2006 19-1998 is eight years. That's still going to be squared plus 3,247. I can subtract 3247 from both sides and When I do that 5836 -3247 is 2589 equals a times eight squared eight squared to 64. So that gives me 64 Times my stretch factor. If I divide both sides by 64, 2589 Divided by 64 will give me my stretch factor. And when I put that into a calculator I get that that stretch factor a equals About 40.4. So value that I've calculated from this gives me 40.4. I'm going to go back to my graph And just check and see if that actually makes sense. Let's go back to Dez most if my a value is about 40, it fits This endpoint. If I put in 40.4 it does go through this end point but it's a little low. It doesn't include all of the other points which is never going to happen with real data. You're never going to get the curve that goes through all of the points exactly. But all of these points are above the curve which means that my model is a little love. I want to model that kind of includes all of the data. It doesn't have to go through all of the data so much as it goes through the middle of all of the data. So I'm going to try just a slightly larger value. 44. I've got one point that's too low and I've got three points that are above 45 is a little closer to the points that are above 46. Dance around 2048. It's kind of like 48 each. That's too big. Just testing to see what looks like balances the points the most. I think maybe like 48 is a good middle of the road. I've got three points that are a little above the curve. I've got one point that's quite a bit below the curve. So I would say a is anything between 44 and 48 is going to be a good model. I personally like 48. So I'm going to say about my model for this data. Yes. My health put value. Why Is equal to 48- nine years? My input year X- My starting year, 1998. Yeah. All squared plus. You make that squared better plus a shift up of 5,836. And that is my quadratic model for this data. Yeah.

Now we're told that this question is very similar to the last. Except in this case, we're told that the starting salary is $2000 and they're going to get a raise of $100 every four months for three years. So we want to know what's going to be their salary at the end of this time. So let's think of this like a sequence. Well, because we're looking for the salary in three years, not the total that they've made. That means we're trying to find a sev ent. We're trying to find the particular terms in the sequence while we know that they're starting off with $2000. So then four months later, they're gonna make an extra $100 so they'll be making $2100. Well, not $21,000 about person would really like it if it was that Well, four months later, which is really means at the end of eight months, let's spell this right. So this means after eight months they're gonna make enough $400 so there are up to 2200. Then if we tack on another four months, which if you think about it. That's after a full year. They're gonna Salary will increase by another $100 which means their salary will be 2300. Well, let's think about this. Pattern is going to continue. So every year was C increase is going to increase by $300 per year. So how much are they going to make at the end of the second year? Well, we're gonna add 300. So that would be 2600 in Let's make that ledge all bull here. 2600. So again, so Afghans of three years, they're gonna make an additional $300. So 2900. So perfect. Now we found that the ends of three years, they will be making $2900 a month.


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