Example 1:
You are considering two used phones for purchase. The cost of the first phone can
be modeled with the function , and the cost of the second
phone can be modeled with the function , where is the time
in years. Your budget is limited, and you plan to buy the less expensive phone in
the next 3 years.
Which statement below best represents the outcome?

You buy the first phone.

You buy the second phone.

Both phones cost the same amount.

Ask by Barber Cervantes. in the United States

Nov 14,2024

Question

Example 1:
You are considering two used phones for purchase. The cost of the first phone can
be modeled with the function , and the cost of the second
phone can be modeled with the function , where is the time
in years. Your budget is limited, and you plan to buy the less expensive phone in
the next 3 years.
Which statement below best represents the outcome?

You buy the first phone.

You buy the second phone.

Both phones cost the same amount.

Ask by Barber Cervantes. in the United States

Nov 14,2024

UpStudy AI · Accepted Answer

To determine which phone is less expensive after 3 years, we need to evaluate both functions $$ f(t) $$ and $$ g(t) $$ at $$ t = 3 $$.

1. **Calculate the cost of the first phone after 3 years:**
   $$
   f(3) = 1,500(0.8)^{3}
   $$
   $$
   f(3) = 1,500 \times 0.512 = 768
   $$

2. **Calculate the cost of the second phone after 3 years:**
   $$
   g(3) = 2,000(0.6)^{3}
   $$
   $$
   g(3) = 2,000 \times 0.216 = 432
   $$

Now we compare the two costs:
- Cost of the first phone after 3 years: $$ f(3) = 768 $$
- Cost of the second phone after 3 years: $$ g(3) = 432 $$

Since $$ 432 < 768 $$, the second phone is less expensive after 3 years.

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