Question

Revenues of software publishers in a country for the years 2004-2018 can be modeled by the function S()=91.412e⁰.⁰⁵¹⁷⁵ˣ , where =4 represents 2004, =5 represents 2005, and so on. What does S(12) represent in this context?

Answer 1

In the context of the given function
`\( S(x) = 91.412e^(0.05175x) \), \( S(12) \)`represents the estimated revenues of software publishers in the country for the year 2016.

Step-by-step explanation:

The function
`\( S(x) = 91.412e^(0.05175x) \)` models the revenues of software publishers for the years 2004 to 2018, where x corresponds to the number of years since 2004. To find
`\( S(12) \)`, substitute
`\( x = 12 \)` into the function:

`\[ S(12) = 91.412e^(0.05175 * 12) \]`

Now, calculate the exponent:

`\[ S(12) = 91.412e^(0.621) \]`

Using the value of
`\( e \approx 2.71828 \)`, we get:

`\[ S(12) = 91.412 * 1.861 \]`

Finally, the estimated revenues for the year 2016 can be found by multiplying these values:

`\[ S(12) = 170.101 \]`

Therefore
`, \( S(12) \)` is approximately 170.101, representing the estimated revenues of software publishers in the country for the year 2016.

This means that, according to the given model, the projected revenues in the 12th year (2016) are expected to be around $170.101 million. The exponential growth nature of the function suggests that the revenues increase rapidly over the years, indicating a positive trend in the software publishing industry during this period.