Question

The temperature of a chemical solution is originally 21^\circ\text{C}21 ∘ C. A chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{C}75 ∘ C after 1212 minutes of heating. The temperature, TT, of the solution in ^\circ\text{C} ∘ C is a function of xx, the heating time in minutes. Write the function's formula.

Answer 1

Answer: The required function is,

T(x) = 21 + 4.5 x

Step-by-step explanation:

The original temperature of the solution = 21° C

Let the temperature is increasing with a constant rate of y degree per minutes,

Thus, the temperature of the solution after 12 minutes = 21 + 12 y

According to the question,

21° + 12 y = 75°

⇒ 12 y = 54°

⇒ y = 4.5°

Hence, the constant rate of increasing the temperature = 4.5° per minutes,

Thus, the temperature of the solution after x minutes,

T(x) = 21 + 4.5 x

Which is the required function.