Answer: T = T env + Ce -kt.
- A T = T<sub>env</sub> + Ce<sup>-kt</sup>
- B T = Ce<sup>kt</sup>
- C T = T<sub>env</sub> - kt
- D T = T<sub>env</sub> + kt
Correct answer: A. T = T<sub>env</sub> + Ce<sup>-kt</sup>
Explanation: Let u = T - T<sub>env</sub>. du/dt = -ku. u = Ce<sup>-kt</sup>. T = T<sub>env</sub> + Ce<sup>-kt</sup>.
The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.
Concept context
Equations involving derivatives and their solutions