Example 4:
You are interested in two second-hand gaming consoles. The first console’s price is
given by the function , and the second console’s price is given
by , where represents the time in years. Your budget
constraints require you to choose the more affordable option within the next 2
years.
Which statement below best represents the outcome?

You buy the first console.

You buy the second console.

Ask by Chambers Tyler. in the United States

Nov 14,2024

Question

Example 4:
You are interested in two second-hand gaming consoles. The first console’s price is
given by the function , and the second console’s price is given
by , where represents the time in years. Your budget
constraints require you to choose the more affordable option within the next 2
years.
Which statement below best represents the outcome?

You buy the first console.

You buy the second console.

Ask by Chambers Tyler. in the United States

Nov 14,2024

UpStudy AI · Accepted Answer

To determine which console is more affordable within the next 2 years, we need to compare the prices of the two consoles at $$ t = 2 $$ years.

Given:
- The price function for the first console is $$ f(t) = 600(0.75)^t $$.
- The price function for the second console is $$ g(t) = 800(0.6)^t $$.

We need to find the prices of both consoles at $$ t = 2 $$ years and compare them to determine which one is more affordable.

Let's calculate the prices of both consoles at $$ t = 2 $$ years:

1. For the first console:
$$ f(2) = 600(0.75)^2 $$

2. For the second console:
$$ g(2) = 800(0.6)^2 $$

Now, we will calculate the prices of both consoles at $$ t = 2 $$ years.
Calculate the value by following steps:
- step0: Calculate:
  $$600\times 0.75^{2}$$
- step1: Convert the expressions:
  $$600\left(\frac{3}{4}\right)^{2}$$
- step2: Evaluate the power:
  $$600\times \frac{9}{16}$$
- step3: Multiply:
  $$\frac{675}{2}$$
Calculate or simplify the expression $$ 800*(0.6)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$800\times 0.6^{2}$$
- step1: Convert the expressions:
  $$800\left(\frac{3}{5}\right)^{2}$$
- step2: Evaluate the power:
  $$800\times \frac{9}{25}$$
- step3: Multiply:
  $$288$$
The price of the first console at $$ t = 2 $$ years is $$ \frac{675}{2} $$ or 337.5, and the price of the second console at $$ t = 2 $$ years is 288.

Since 288 is less than 337.5, the second console is more affordable within the next 2 years.

Therefore, the statement that best represents the outcome is:
- You buy the second console.
You buy the second console.

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