An object with initial temperature $180^{\circ} \mathrm{F}$ is submerged in large tank of water whose temperature is $60^{\circ} \mathrm{F}$. Find a formula for $F(t)$, the temperature of the object after $t$ minutes, if the cooling constant is $k=0.6$ \[ F(t)= \] Question Help: Video $\square$ Message instructor Submit Question

Step 1 ：An object with initial temperature $180^{\circ} \mathrm{F}$ is submerged in large tank of water whose temperature is $60^{\circ} \mathrm{F}$. We are asked to find a formula for $F(t)$, the temperature of the object after $t$ minutes, if the cooling constant is $k=0.6$.

Step 2 ：We can use the formula for Newton's law of cooling, which states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. The formula is given by $F(t) = T_a + (T_0 - T_a) \cdot e^{-kt}$, where $T_0$ is the initial temperature of the object, $T_a$ is the ambient temperature, $k$ is the cooling constant, and $t$ is the time.

Step 3 ：Substituting the given values into the formula, we get $F(t) = 60 + (180 - 60) \cdot e^{-0.6t}$.