1. **State the problem:** A thermometer starts at 21 degrees indoors and is taken outside to -7 degrees. After 1 minute, it reads 14 degrees. We need to find the temperature reading after $t$ minutes. 2. **Model the problem:** This is a Newton's Law of Cooling problem, which states temperature $T(t)$ changes according to $$\frac{dT}{dt} = -k(T - T_\text{env})$$ where $T_\text{env} = -7$ degrees is the environment temperature. 3. **General solution:** The solution is $$T(t) = T_\text{env} + (T_0 - T_\text{env}) e^{-kt}$$ with initial temperature $T_0 = 21$. 4. **Use given data to find $k$:** At $t=1$, $$14 = -7 + (21 + 7) e^{-k}\Rightarrow 14 = -7 + 28 e^{-k}$$ 5. **Solve for $k$:** $$14 + 7 = 28 e^{-k}$$ $$21 = 28 e^{-k}$$ $$e^{-k} = \frac{21}{28} = \frac{3}{4}$$ $$-k = \ln\frac{3}{4}$$ $$k = -\ln\frac{3}{4} = \ln\frac{4}{3}$$ 6. **Find $T(t)$:** $$T(t) = -7 + 28 e^{-kt} = -7 + 28 \left(e^{-k}\right)^t = -7 + 28 \left(\frac{3}{4}\right)^t$$ 7. **Final temperature reading after $t$ minutes:** $$\boxed{T(t) = -7 + 28 \left(\frac{3}{4}\right)^t}$$ This formula lets you calculate the temperature at any time $t$ after being taken outdoors.