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Math  /  Algebra

QuestionThe temperature, tt, in Burrtown starts at 25∘F25^{\circ} \mathrm{F} at midnight, when h=0h=0. For the next few hours, the temperature drops 3 degrees every hour.
Which equation represents the temperature, tt, at hour hh ? A. t=−25h+3t=-25 h+3 B. t=−3h+25t=-3 h+25 C. t=3h+25t=3 h+25 D. t=25h−3t=25 h-3

Studdy Solution

STEP 1

1. The initial temperature at midnight (when h=0 h = 0 ) is 25∘F 25^{\circ} \mathrm{F} .
2. The temperature decreases by 3∘F 3^{\circ} \mathrm{F} every hour.
3. We need to find an equation that represents the temperature t t at any hour h h .

STEP 2

1. Identify the initial condition.
2. Determine the rate of change.
3. Formulate the equation.
4. Verify the equation with given options.

STEP 3

Identify the initial condition.
At h=0 h = 0 , the temperature t=25∘F t = 25^{\circ} \mathrm{F} .

STEP 4

Determine the rate of change.
The temperature decreases by 3∘F 3^{\circ} \mathrm{F} per hour, which means the rate of change is −3 -3 degrees per hour.

STEP 5

Formulate the equation.
The equation for the temperature t t at hour h h can be written as: t=initial temperature+(rate of change×h) t = \text{initial temperature} + (\text{rate of change} \times h) t=25−3h t = 25 - 3h

STEP 6

Verify the equation with given options.
The equation t=25−3h t = 25 - 3h matches option B: t=−3h+25 t = -3h + 25 .
The correct equation is: t=−3h+25 \boxed{t = -3h + 25}

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