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The table shows the numbers $N$ of college-bound seniors intending to major in engineering who took the SAT exam from 2008 through $2013 .$ The data can be modeled by the logarithmic function $$N=-152,656+111,959.9 \ln t$$

where $t$ represents the year, with $t=8$ corresponding to 2008 . (Source: The College Board)

$$\begin{array}{|c|c|}\hline \text { Year } & \text { Number } N \\\hline 2008 & 81,338 \\2009 & 88,719 \\2010 & 108,389 \\2011 & 116,746 \\2012 & 127,061 \\2013 & 132,275 \\\hline\end{array}$$

(a) According to the model, in what year would 150,537 seniors intending to major in engineering take the SAT exam?

(b) Use a graphing utility to graph the model with the data, and use the graph to verify your answer in part (a).

(c) Do you think this is a good model for predicting future values? Explain.

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University of Michigan - Ann Arbor

it is given that decoration and is equal to B minus 152 656 plus 111959.9 Loki, where n represent the We're n represent Our college bound seniors and t represent the year. Now we need to find the year. Then the number off see, college bound seniors is equal to be 150537 now, but putting the value offend in the question we get the Grishin won 50537 is equal to B minus 15 to 656 plus 111959.9 Log T Now we're simplifying it. We get low. T is equal to be 303193 divided by 111959.9. Now, by simply find it, we get the value of two is equal to be approximate 15 years. So in 2015 that bad you Oh, the college bound seniors. Now we need to bloat the graph off the Cuban more than now. The graph we look like as so this is a required ground for the given model. Now the given model is, ah, good model for predicting the future values because we're putting the values off T for future, we can find easily the number off college bound seniors.