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Use the models below that approximate spending in the United States from 1988 to $1997 .$ Let $t$ represent the number of years since 1988 .
Copy and complete the table. Use the rewritten model from Exercise 51 . Round to the nearest thousandth.
$$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Year } t & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline \text { Ratio of } E \text { to } s & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? \\
\hline
\end{array}$$

We have 52 number problem, Mr. Going to copy the complete day. Well, from exercise 51. So from 51 we will be having e by s that is dollars spent on exercise. My total dollars on this force equipment equal toe 200 a d plus 1400 divided by 900 t bless 9900 Solar to stay home. Do that's common to a day plus 14. Divide by 100 that in 90 less 99. This will get cancelled out. So to t plus 4 10 by 90 plus 99 Some 50 amenities. Okay. And, oh, from long division, we have to copy. So we will be using long division to t plus 14 99 9. So it will be nine by two. So sorry to one, and will It will be due by nine. So this will be to t plus 20 to minus minus. This will get cancelled out and it will be minus seven. So this can be organized. Dubai nine bless. Minus seven by 90 plus 99. Okay. Can no. We have to get, um to find the table. Values of table went equal to zero from t equals zero t. It's called nine to thousands. Noticed how thems just start completing. Just like in the value of D. In this equation, it will become do by nine bless minus standby physical plus 99. So this would be 22. I get dual minus seven by 99 which is the king by 99. That is seen by 99 0.15 Missed out 15 one fight So approximately 0.1 fight too. When people to one this will become Do you by name, my ass. We'll get blessed minus sitting by. This is welcome to 18 99 which is 117 It's no become my missus by 1/100 that I'm doomed. Little 0.16 approximately 0.162 Thank equal to two. We will be having by nine less my seven by Okay, Mr. Because this will be even tickled. One. This will not be 18. This will be only 108. This would weigh 108 so 24 minus. This will be 24 minus seven 14 by 108. Oh, you can say ah 20 to minus seven it is 17. Just like, uh, 24 24 minus seven by 108 which means 17 by 108. This 17 divided by 108. It is 0.157 on the approximately 0.157 Okay, But they did not. Yes. 157 Okay, now of antique will do too. This will be, um, one under 17. There it is. 26 minus seven by 117. That is 19 by 117. So my divided by 117 approximately 0.162 meant equal to three to buy nine place, minus seven by one or 17. According to the pattern, it should be 21 by 126. Do you wonder why by 120 suits, which is a little 0.167 approximately on equal to 42 by nine. Bless. Minus seven by the 726. Okay, 135. So this will become 23 by 100 35. 21 had 35. It was approximately 0.170 No, I meant equal to five. This will be controlled by nine players minus seven by one and therefore before. So this will become 25 by 144. Gentrified right by 144 that is little 0.1736 or 17 for approximately. When people go states, this will become to buy nine place minus seven by one city trying to seven by one. And definitely just do it by 150 little point 176 when equal to seven, it would be to buy nine place, minus seven by 1 62. So 29 by 162 29 divided by 162. That makes it a point. Once your name. 21 to 8 by nine players. My son by 171. So 31 by 171. Is it a point? One It one. And when he's 29 you will be helping to buy nine. Let's 97 by 180. That is 40. My 180. Okay, technically, in 14. 33. My one that 80 three d mind by one into ot that little 0.1 80. So did These are the points you have got First foreign, second point in third point. Fourth point 56th. Okay. Okay. Thank you.

With analyzing the different equations, the models for um the different countries, you want to be paying attention to the exponents when we're talking about which country has the greatest growth rate, Because positive means its growth, a negative means it's declining in population, so the largest positive would have been Iraq, and then by what percentage of the population increasing each year, One point, you got to convert this to 1.9%.

Hey, guys. So we have four countries here, and we're looking for the highest growth rate in population. So how can we identify that? So right here we have a formula for the exponential model where a zero is the original amount and Katie rights. Okay, Is he rate of growth or D cake and tease time. So let's just look at the exponents of E and identify the number of multiply T. So the rate here would be all the things that I underlying almost compare them so she can see your point. 0 19 is the highest one, right? So then Iraq would have the greatest girls rate in population and they're asking us to convert that into percentage. So simply multiply that by 100 and then you go. The percent rate here would be 1.9%. So in other words, by

So this question we are given a model with the equation. Why is 35 5/4 to the far off? Do you? Just the same as 35. 1.25 to the power off. Yeah. First, we're asking this user growth for K model. So we see that are factor. Here is more than one call factor. So this is a exponential growth Mano, Our growth factor we see is this valley of here is 1.25 on the percent increase. So basically, we have this expression one was are supposed to 1.25 Our 0.254% increase here is 25%. Next, the answer to that question on just to keep things in the same notation instead of 1.25 we can also say that the gold factor is higher