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

The following table shows a company s annual income over a 6 year period The equation y 60000 1 2 x describes the curve of

Answer :

The company's approximate annual income for the year 2009, using the given exponential growth model, would be $257,989.02.

The closest option to this calculated value is $258,000.

The correct option is (C).

To find the company's approximate annual income for the year 2009 using the given equation:

1. Identify the given information: The equation for the annual income is [tex]\( y = 60000 \times (1.2)^x \)[/tex], where ( x ) is the number of years since 2001.

2. Calculate the value of ( x ): Since we want the income for the year 2009, ( x ) would be 2009 - 2001, which is 8.

3.Substitute the value of ( x ) into the equation to find ( y ), the approximate annual income for the year 2009.

Let's perform the calculation:

[tex]\[ y = 60000 \times (1.2)^8 \][/tex]

Now, we'll compute the value using the provided equation.

The company's approximate annual income for the year 2009, using the given exponential growth model, would be $257,989.02.

The closest option to this calculated value is $258,000.

Thanks for taking the time to read The following table shows a company s annual income over a 6 year period The equation y 60000 1 2 x describes the curve of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Given that the annual income of a company over a 6-year period is described by the equation:

[tex]\begin{gathered} y=60000(1.2)^x \\ \text{where} \\ x\text{ is the number of years since 2001} \end{gathered}[/tex]

The annual income at the end of each year since 2001 is as shown in the table below:

Required: To evaluate the company's approximate annual income in 2009.

Solution:

Given the annual income described as

[tex]y=60000(1.2)^x[/tex]

The number of years between 2001 and 2009 is evaluated as

[tex]x\text{ = 2009 -2001 = 8 years}[/tex]

thus, it's been 8 years since 2001.

The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.

This gives

[tex]\begin{gathered} y=60000(1.2)^x \\ x\text{ = 8} \\ \text{thus,} \\ y\text{ = 60000}\times(1.2)^8 \\ =\text{ 60000}\times4.29981696 \\ y=\text{ }257989.0176 \\ \Rightarrow y\approx258000 \end{gathered}[/tex]

Hence, the company's approximate annual income in the year 2009 will be $ 258000.

The third option is the correct answer.