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In 1975 bought an old Martin ukulele for $200_ In 1995similar uke was selling for $800. In 1980 pought new Kamaka Uke for $75. In 1990, sold it for $325,(a) Give li...

Question

In 1975 bought an old Martin ukulele for $200_ In 1995similar uke was selling for $800. In 1980 pought new Kamaka Uke for $75. In 1990, sold it for $325,(a) Give linear model relating tne price of the Martin Uke to the Year Takein 1975p(t){b) Give linear model relating the price of the Kamaka uke to the year Again takein 1975_g(t)(c) In what year is the value of the Martin twice the value of the Kamaka?(d) Give function flt) which gives the ratio of the price of the Martin to the price of the Ka

In 1975 bought an old Martin ukulele for $200_ In 1995 similar uke was selling for $800. In 1980 pought new Kamaka Uke for $75. In 1990, sold it for $325, (a) Give linear model relating tne price of the Martin Uke to the Year Take in 1975 p(t) {b) Give linear model relating the price of the Kamaka uke to the year Again take in 1975_ g(t) (c) In what year is the value of the Martin twice the value of the Kamaka? (d) Give function flt) which gives the ratio of the price of the Martin to the price of the Kamaka In the long Tun what will be the ratio of the prices of the Martin ukulele to the Kamaka ukulele?



Answers

A corporation has three factories, each of which manufactures acoustic guitars and electric guitars. The production levels are represented by $A$ .
$A=\left[ \begin{array}{ccc}{70} & {50} & {25} \\ {35} & {100} & {70}\end{array}\right]$
(a) Interpret the value of $a_{22}$
(b) How could you find the production levels when production is increased by 20$\% ?$
(c) Each acoustic guitar sells for $\$ 80$ and each electric guitar sells for $\$ 120 .$ How could you use matrices to find the total sales value of the guitars produced at each factory?

In the first part. The one and we want is equal Zito and relevant it do you do, We do is do. And 6 50 now using M is he will do the two minus we want Do you want to buy it? De tu minus The one is equal to 6 50 minus well 100. You want to buy Tu minus Tzeitel? Is it Will do minus to 75? Yes, we is equal to minus 2 75 p Bless Well, no wonder in the second part Yeah, p is equal toe do And why is equal to 6 50 6 50 is equal Do 1200 multiplied by e. This is the part minus Do be lawn 30 in the word white 24 is equal Do minus will be lan e It is equal to be equals 20 fine 3066 As we is equal to 1200 e a symbolic minus zero point to the Tzeitel 66 Be no in Farsi. The graph off the following with me. Take this This lane. It's what we is equal to. So 75 be less well under And this line It's for B is equal to 1200. Erase the wallet minus zero point that easy. It'll sink six Be no in the fourth part. Exponential more than the police years faster and forced to. Yet in fifth part from graph lenient is greater on zero less than p less than I do and exponential greater on be greater than you could do being.

This question is having a look at a consumer price index or CPI when we're comparing the costs of Guillem service over years. So in um 1983 which crosses T equals zero. Our cost $100. And in 2010 Um which would be 2010, 1983 equals 27. Our cost is 216. They want to fit an exponential model to this um where case and five decimal places we're going to say Um 216. He was 100 E. To the Right Times 27. So um to 16 over 100 divided by 100. This is 2.16. You call the 827 are So natural log 2.16 27 are R equals I'm going are the book calls it K. It's the same same variable. So the five different places. Yeah zero two A 52 Yeah. So now we can go ahead and we can write the actual function. Um We're going to call it C. 100 mm .0285- 18. This is part a Part B. Has this looking at um what it will cost in 2020. So see it's going to 100 0285. two times. We take 2020 -1983 which gives us 37. So we have E raised .02852 Time is 37 times 100 Gives us 2 87 0.27 This is A. B. Now see is asking us um to find one that costs double formal cost 200. I want to raise some of this to give us some room and we're gonna go ahead and look at parts seat. Right? So apart C. know our final cost as 200 double what we started with. We know our rate, we know our initial so we're looking for the time. So what that process looks like here, We'll go ahead and do it. You're doing green 200. It was 100 8.02852 times team mm two. It was e .0285 to T. Natural Log of 2.0285 to T. So T becomes equal the nighthawk of two, Divided by .02852, Which became was 24 point 30 years. Let's see.

All right. So for problems 76 we need to come up with a linear equation that relates to the situation and on situations that a company is making money. And in its first year, your one it makes $30,000 $30,000 on in its second year or sorry. In its fourth year, it makes $66,000. So, uh, we're gonna make a linear equation here using why equals MX plus B and we can start by finding the slope. So remember, slope, it's gonna be changin. Why? Over change in X, which will really for this situation be 66,000 minus 30,000. Fix that, um, over four minus one s. So what does that come out too? Well, that's gonna give us $36,000 over three or 12,000 So that is going to be our slope in this scenario. So if we now complete bed in so we get why equals 12,000 x plus B. And now we consult for B by using one of these given equations. So if we use 30,001 we can use 30,000 equals 12,000 times one plus B and then we subtract that over and that will give us 18,000 equals on. Now we can write our final equation, So why equals 12,000 X plus 18,000 on. So this is now an equation that for a given, you will tell us the amount of profit we're gonna make So we can, you know, going to part beat, in which we need to find out what the prophet is in its seventh year. So we need to plug 17 for X. So why equals 12,000 time seven plus 18,000. So let me just see what that comes out to here. So that will be 100 in $2000. So in your seven, they will make that much money on. Now, finally, we need to see for part C what the what year it will be when the company makes $126,000. So we can set 126,000 equal to our equation of 12,000 x plus 18,000 and we can start by moving this 18,000 over. To get this idol will leave us with 102,000 dollars equals 12,000 x And now if we divide 102,000 by 12,000 that will give us eat 0.5 equals X. So it says so it asks when the profit will reach 100 26,000 and you can't reach it in half a year. So we're gonna round that up to nine years is when we will reach that profit.

We're given the rate of textbook and the inflation rate in 1984 part A. We have to fight the formula be Sebti or the price of picks Books starting at the price of tape textbook in 1980 piece of zero times E to the R T where are is you know, poi 0 67 times Eat because the raid here is exponentially growth or continuous in part B, we need to fight the formula for the price of a new item even that the price of an item piece of zero in 1980 terms e Teoh in flash and rate is your poison or 33 t. And finally, if with the textbook caused $50 which is piece of zero is if the bien the price, the textbook will be double given that, uh, resulted fourth for Murthy in flash in. So we're gonna have police empty ego to 50 e to the 0.0 60 70 and so this is a textbook price. After tea years been, This result is affected by the inflation rent, so the ticks full price, it will be double resulted for the inflation. So be to terms Freedy in. We're gonna apply the formula, form the inflation. It's 0.0 33 t and then we're gonna so 40 place on these equation. So I have the 50 on both sigh cancel out. So he I have to heat 0.33 t e to the 0.0 60 70 And then when a divided both side by eases your poison 33 t So these cancel So on the left side I have e to the so sooner poi 0 30 40 So I take serial poisoner off 60 seventies of trying zero poi 0 33 t and I got this You go to to and I'm gonna take the national on both sides. So on the left side get 0.0 30 40 he go to you boys 693 and then by dividing both sides by 0.0 34. So these give me t is 20.4 years. So after 10 years 0.4 years since 1980 the textbook prize will be double, given that the in flat and breathe is 3.3%


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