Question

Based on this information, which function best models the number of game consoles sold in
millions x years since 2009?
(1 point)
g(x) = 0.6(25.5)
x
g(x) = 25.5(0.6)
x
g(x) = 6.12(25.5)
x
g(x) = 25.5(6.12)
x

Answer 1

To determine which function best models the number of game consoles sold in millions \( g(x) \) with \( x \) years since 2009, we need to analyze the structure of each function provided.

Here's a breakdown of the functions:

1. **g(x) = 0.6(25.5)^x**: This suggests that the quantity starts at \( 0.6 \) million and grows exponentially based on \( (25.5)^x \).

2. **g(x) = 25.5(0.6)^x**: This indicates an initial sale of \( 25.5 \) million, but it declines over time since \( (0.6)^x \) represents an exponential decay.

3. **g(x) = 6.12(25.5)^x**: This implies starting at \( 6.12 \) million with growth based on \( (25.5)^x \).

4. **g(x) = 25.5(6.12)^x**: This suggests \( 25.5 \) million initially, growing exponentially based on \( (6.12)^x \).

From the context, if we assume that game console sales are expected to grow over time, a function that reflects growth starting from a somewhat reasonable initial sale amount would be more appropriate.

The best choice, therefore, likely depends on initial values expected for console sales and growth trends in the gaming console market.

If we assume substantial sales initially followed by exponential growth, then **g(x) = 25.5(0.6)^x** would suggest a decline, which may not reflect the gaming market trend.

The choice that best suggests growth from a reasonable initial amount would likely be:

**Answer: g(x) = 6.12(25.5)^x**

This indicates there’s a strong initial sales number that grows significantly over time, aligning best with market expectations for a product that typically sees increasing sales through marketing and new releases.

However, please clarify or provide more context regarding hardware sales trends for a precise selection.