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World conjuroooon of 3nc runnino160.062t million metric tons per year Ehctcris the number Years Ence 2011 the rate (Round You: coniticients three drdimal places } F...

Question

World conjuroooon of 3nc runnino160.062t million metric tons per year Ehctcris the number Years Ence 2011 the rate (Round You: coniticients three drdimal places } Finde Fomulittor (Ni tDamnaunzOltinc consimad mithin yeany 2014clt) 5conuici at te rate, when ( n vears since Z0110 will the known resoufces 255 milion Metric ton ot Zin conalmoton proiocdye cobrinaitor Iron and #ud Round Your ansncr one decina piace;) Yeartexhausted? (Zinc /Mnnn

World conjuroooon of 3nc runnino 160.062t million metric tons per year Ehctcris the number Years Ence 2011 the rate (Round You: coniticients three drdimal places } Finde Fomulittor (Ni tDamnaunzOltinc consimad mithin yeany 2014 clt) 5 conuici at te rate, when ( n vears since Z0110 will the known resoufces 255 milion Metric ton ot Zin conalmoton proiocdye cobrinaitor Iron and #ud Round Your ansncr one decina piace;) Yeart exhausted? (Zinc / Mnnn



Answers

By how many metric tons did the amount of zinc produced increase between 1990 and $2007 ?$

In this problem, we want to convert four million metric tons into grams and were given that one metric ton is equivalent to 1000 kg. So we're gonna go ahead and start with that. The one metric ton is equal to 1000 kg. We're going to use that fact to kind of help us. So we know again one metric ton is equal to 1000 kg, But we know that one kg There are 1000 g present. So in order for us to essentially find out um how many grams are in 1000 kg, all we have to do is multiply our 1000 g um times 1000 kg. Um So again, so in 1000 kg we can multiply one johnson times mhm 1000. Right, so 1000 programs times 1000 g and per kilogram that's going to give us one million France. So let's go ahead and simplify this and just kind of make sure this writes out a little bit better. So in one million rhetoric cons and you know, in one really make a ton in terms of grams that we're going to have because all we did was just figure out how many grams are present. And essentially the one metric ton. Right? And so we're gonna go ahead and multiply one million ton. Right? So one million? Make sure we have any six zeros here times the number of grams present in one metric time. Which is a million. That's going to give us a big number. It's going to have a total of 12 zeros 8, 3, 6, 9, 12. Perfect cramps. So we have a total of uh, this many grams per one metric ton. But we have four million metric tons. So we have to do is just multiply this by four. And so our overall Number of g and four million or four million metric guns is going to be 34. And we have to add 4,012 Zeros After it is the 3, 6, 9, 12. Perfect. There we go. We found that the number of grams here in four million metric tons.

Mhm. So 36 billion metric tons of C. 02 um Get released worldwide uh each year. And so let's try to get that into grams. um well 36 billion is 36 now Billion is times 10 to the nine. Okay, metric tons. And of course we don't like having 36 before scientific notation. So we'll move the decimal place over one and we'll say it's 3.6 times 10 to the 10 metric tons. Now let's convert metric tons. Um 1000 kg is the same as a metric ton And 1000 g are in a kilogram. So if we cancel out metric tons, we cancel out kg will get g. And if you were to plug this into a calculator you would get 3.6 times 10 to the 16 g. But we don't want it in scientific notation. We want to use our metric prefixes. So the closest metric prefix we have to, this is Peta and Peter Is 10 to the 15 of something. So how do we get this value into times 10 to the 15? We've got to move the decimal point over one to the right. That would give us 36 times 10 to the 15. Okay, as a value. So what can we do with this? Well if we take our 36 times 10 to the 15 and we take the fact that Peta is 10 to the 15. We can say that we have 36 pentagrams of co two

So let's start with um an equation called Sea of capital T. So we're going to let that be equal to total copper mine. Okay so now lower case T. Is number of years since 2014. Mhm. Okay so that means In 2014. So see of zero would be zero. Because we haven't started mining any copper yet. And they were also given an expression for the rate at which corporate is being mine. So now part A. Were asked to come up with an expression that gives us the total quantity mind in the first two years. So that's going to be C. Of T. Is equal to The integral from zero. Cool. of the rate at which copper is mined which is 17 lying times E. To the power of 0.20 25 Okay so this is the expression so now part B. Says under these assumptions meaning if harper continues to be extracted at that rate. When is the world addicted to run out of copper? Okay. So we're told that in the beginning of the year 27 started 2014, Um it is known that the world has a total copy reserve of 600 and Monday million times. Okay. And this expression is also given to listen millions. So we're basically trying to figure out what this capital T. When this CFT Is all of our reserve which is 690. So let's first actually find this interval. Mhm. So see Of T. is equal to the integral of that. So let's go ahead and find that that's going to be 17.9. And we have e. to the 0.025 p. And then we had to multiply by one over 0.0 two sides And then we evaluate this from zero to capital T. Okay, so this is going to be 17.9 over 0.025. And then we have He to the 0.025 times capital T minus either. The zero. Which is when Okay, so this is our expression for CMp. So now we need to calculate capital T for when this is equal for 690. So let's go ahead and do that. We're working for 690 in and this is equal to 17.9 over 0.025 times. Eat the 0.025 T minus one. And now we just have to isolate capital T. So we're going to multiply both sides. Bye. The reciprocal of this. So that will be times .025 Divided by 17.9. And then we're going to add one to both sides. So right now we have one 96 is equal to E 0.025 T. And then we're going to take the natural algorithm of both sides. So then we get A decimal number is equal to 0.025 teas. All we have to do is divide both sides by 0.025. And we get that T is Roughly it was 26.99 27. Okay, so we're not done yet because this is just a number of years since 2014. The question Asks us when right? So if we just say 27, that doesn't actually mean anything. So we need to give an actual year. So what that means is that's 27 years after The beginning of 2014. So you basically just add 27 2014 and then you should get in a year 2000 and 41.

So we're gonna be using similar numbers or similar formulas were talking about copper this time. So we're gonna change 23.1 to 12.6. We're gonna change 6 34,050 or and change. Uh, 0.32 point 024 And so that our, uh, formula now and that tells us that it will be until 2032 that the re sources are depleted. Um, if, however, the reserves were twice this amount s 06 52 1300 that tells us that would take until 2050 close of 2051 to deplete those resource is. And then, um, if the world reserves remained at 6 50 and then we want to sit, subtract the consumption of that, receive that it would only take 51 years, uh, to I deplete the resource is of, um, cover


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