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Cingr the number (in billions) monihly text messanes Dven [ he euanon Ie gnrorimate "028.3 -15.3 number ol yuars since Zd00. 2002 znere Were apprOunaleur Eilli...

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Cingr the number (in billions) monihly text messanes Dven [ he euanon Ie gnrorimate "028.3 -15.3 number ol yuars since Zd00. 2002 znere Were apprOunaleur Eillicn mortn; Iex Meaeges Complete Pans 4 Ftad Tten Hnen represeris [Fudur icuon tha ONlsine lotn numbtthillian'|montalytuxt Meseaq05 In Yua4ua Acccrding this funcbon, hox Many monlna lea[ Messages wete (nue 2009?billion

cingr the number (in billions) monihly text messanes Dven [ he euanon Ie gnrorimate "028.3 -15.3 number ol yuars since Zd00. 2002 znere Were apprOunaleur Eillicn mortn; Iex Meaeges Complete Pans 4 Ftad Tten Hnen represeris [ Fudur icuon tha ONlsine lotn numbtt hillian'| montalytuxt Meseaq05 In Yua 4ua Acccrding this funcbon, hox Many monlna lea[ Messages wete (nue 2009? billion



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Approximately 160 billion text messages were sent worldwide in 2000 . Since then, the number of text messages sent each year has grow by about $33 \%$ per year. How many text messages were sent worldwide from 2000 through $2010 ?$

Okay, so I've prime a T R. Function is the approximate rate of change in a number of monthly taxes. Okay, So for part A were asked to find the total number of the monthly Texas. So that's just the inter girl of our rate of change for our text messages. So that's the integral of F property G. So let's start by finding that. Okay, So using our defence role, get the fallen. Okay, I notice here that we have some constants inside are integral, so we can use our constant multiple rule to bring them outside. Okay, so that gives us, um, seven points 50 All teeth depart to over to find a 16.8 T plus a constant K. So this is our half of tea, which is? They told a number of Texas text messages it in a year. Teeth notice here that we have okayed, okay, but were also given this following piece of information that would help us saw for kids were given that to 2005. If that is valued at five, we have 9.8 billion monthly taxes. That's equal to 9.8. Okay, so let's use that song for King. So we have 9.8 is equal to 7.50 T, which is five squared over two when a 16.8 times five kit. Okay, so I'll put that into my calculator and see what I get. So this is 9.75 In case of 9.8 minus 9.75 That's equal to 0.5 is you go to K. So our function for monthly Texas is F A T is equal to 7.5, divided by two. That's 3.7522 to minus 16.8 t and n plus K, which is 0.5 Okay, so this is our solution to part pay. And for part B, we want to find the total amount of monthly Texas when our year is equal to that of the night. Notice that are. You starts at 2000. So at 2000 R T value is equal to zero. So that means, um, at 2009 that's nine minus 2000 that secret to nine. So this is when t is equal tonight. So we have f at to use equal to nine is equal to two falling. I'm just gonna plug in. It replaced t would nine in our equation. Okay. And I'll plug this into my calculator and see what I get. So he gets, um 152.6 1,000,000,000 number of Texas in 2009.

This problem. We're told that the total number of email messages sent per day in 2000 and eight equals a whopping 210 billion messages and a lot it was 210 billion is really the sum of two types of messages spam and non spam messages. So we're also told the problem that the number of spam messages it's about five times greater in the number of non spam messages. Unfortunately, so if I could represent funnies Youth letter acts to represent the total number of non spam messages, they can use five backs to represent the total number of spam messages in Spain. Messages out perform non spent messages by five times. Now. Our goal is to find the number of both non spans fan messages, the seven equation that release into the sun. So if we say, X plus five acts is equal to the total number of messages 210 billion being soft Rex is to be six x is to 10 billion, divide both sides by six isolate x x Just the number of non spam messages equals 210 billion over six jiggles 35 billion messages that is a time a lot now when you calculate how many not how many spam messages do we get spam messages? It's five acts. We're just five times 35,000,000,035 bill. Five eggs. Just think about five times 35 regal 210 1,000,000,000 messages that are span. Sorry, not to 10. Let me redo that. 35 1,000,000,000 multiplied by five equals 1 75 It's erase that. Do you test, son? 1 75 It's a component of that's that span, so summary. Your 175 billion messages are spam and 35 billion non spam messages. Add those two numbers. Together we do get 210 billion, which

Chlorofluorocarbons or otherwise, CFC's are.

The number one trillion is one times 10 to the 12th. Written in standard form is one followed by 12 zeros.


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