Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

The temperature, [tex]t[/tex], in Burrtown starts at [tex]32^{\circ} F[/tex] at midnight, when [tex]h = 0[/tex]. For the next few hours, the temperature drops 2 degrees every hour.

Which equation represents the temperature, [tex]t[/tex], at hour [tex]h[/tex]?

A. [tex]t = 2h + 32[/tex]
B. [tex]t = -2h + 32[/tex]
C. [tex]t = 32h - 2[/tex]
D. [tex]t = -32h + 2[/tex]

Sagot :

To determine which equation accurately represents the temperature, [tex]\( t \)[/tex], in Burrtown at hour [tex]\( h \)[/tex], let's analyze each option step-by-step based on the given information.

### Given Information:
- The initial temperature at midnight ([tex]\( h = 0 \)[/tex]) is [tex]\( 32^\circ \)[/tex]F.
- For every hour after midnight, the temperature drops by [tex]\( 2^\circ \)[/tex].

### Equation Analysis:

#### Option A: [tex]\( t = 2h + 32 \)[/tex]
- Initial Condition (when [tex]\( h = 0 \)[/tex]):
[tex]\( t = 2(0) + 32 \Rightarrow t = 32^\circ \)[/tex]F.
- Temperature Drop: When [tex]\( h = 1 \)[/tex], [tex]\( t = 2(1) + 32 = 34^\circ \)[/tex]F. This is an increase, not a drop.

Since the temperature rises with increasing [tex]\( h \)[/tex], this equation is not correct.

#### Option B: [tex]\( t = -2h + 32 \)[/tex]
- Initial Condition (when [tex]\( h = 0 \)[/tex]):
[tex]\( t = -2(0) + 32 \Rightarrow t = 32^\circ \)[/tex]F.
- Temperature Drop: When [tex]\( h = 1 \)[/tex], [tex]\( t = -2(1) + 32 = 30^\circ \)[/tex]F. This is a drop of [tex]\( 2^\circ \)[/tex], which matches the given information.

This equation decreases correctly by [tex]\( 2^\circ \)[/tex] per hour, hence it is a valid model of the temperature change.

#### Option C: [tex]\( t = 32h - 2 \)[/tex]
- Initial Condition (when [tex]\( h = 0 \)[/tex]):
[tex]\( t = 32(0) - 2 \Rightarrow t = -2 \)[/tex]F. This does not match the initial temperature of [tex]\( 32^\circ \)[/tex]F at midnight.

Hence, this equation is incorrect.

#### Option D: [tex]\( t = -32h + 2 \)[/tex]
- Initial Condition (when [tex]\( h = 0 \)[/tex]):
[tex]\( t = -32(0) + 2 \Rightarrow t = 2 \)[/tex]F. This does not match the initial temperature of [tex]\( 32^\circ \)[/tex]F at midnight.

Therefore, this equation is incorrect.

### Conclusion
Based on the given conditions and evaluating each equation:

The correct equation representing the temperature [tex]\( t \)[/tex] at hour [tex]\( h \)[/tex] is:

[tex]\[ \boxed{t = -2h + 32} \][/tex]

Thus, option (B) is the correct answer.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.