Questions: Deepa is preheating her oven before using it to bake. The initial temperature of the oven is 75 degrees and the temperature will increase at a rate of 25 degrees per minute after being turned on. What is the temperature of the oven 17 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?

Solution Steps

To solve the problem, we need to calculate the temperature of the oven after a certain number of minutes. The temperature increases linearly with time. We can use the formula for linear growth:

1. For 17 minutes: Use the formula \( \text{Temperature} = \text{Initial Temperature} + (\text{Rate of Increase} \times \text{Time}) \) to find the temperature after 17 minutes.
2. For \( t \) minutes: Use the same formula to express the temperature as a function of \( t \).

To find the temperature of the oven after 17 minutes, we use the formula for linear growth:

\[ \text{Temperature} = \text{Initial Temperature} + (\text{Rate of Increase} \times \text{Time}) \]

Given:

• Initial Temperature = \(75^\circ\)
• Rate of Increase = \(25^\circ\) per minute
• Time = 17 minutes

Substitute the values into the formula:

\[ \text{Temperature after 17 minutes} = 75 + (25 \times 17) \]

Calculate:

\[ \text{Temperature after 17 minutes} = 75 + 425 = 500 \]

To express the temperature as a function of \( t \) minutes, we use the same formula:

\[ \text{Temperature} = \text{Initial Temperature} + (\text{Rate of Increase} \times t) \]

Substitute the known values:

\[ \text{Temperature after } t \text{ minutes} = 75 + 25t \]

Final Answer