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The table below shows a company's annual income over a 6-year period. The equation [tex]$y = 60000(1.2)^x$[/tex] describes the curve of best fit for the company's annual income [tex]$(y)$[/tex]. Let [tex]$x$[/tex] represent the number of years since 2001.

| Year | Income |
|------|-----------|
| 2001 | $58,900 |
| 2002 | $72,400 |
| 2003 | $86,500 |
| 2004 | $103,400 |
| 2005 | $124,400 |
| 2006 | $150,000 |

Using this equation, what would the company's approximate annual income be in the year 2011?

Answer :

Final answer:

The company's approximate annual income in the year 2011 would be approximately $371,232.38.

Explanation:

To find the company's approximate annual income in the year 2011 using the given equation y=60000(1.2)ˣ, we need to determine the value of x. Since x represents the number of years since 2001, we can calculate x by subtracting 2001 from 2011, which gives us x = 10. Now, we can substitute x = 10 into the equation to find the approximate annual income.

Using the equation y=60000(1.2)ˣ, we have:
y = 60000(1.2)10 = 60000(6.1917364224) ≈ 371,232.38

Therefore, the company's approximate annual income in the year 2011 would be approximately $371,232.38.

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