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.
