AP Calculus AB 7.6 Finding General Solutions Using Separation of Variables Questions

At time t=0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal

temperature of the potato is 91 degrees Celsius ( ${ }^{\circ} \mathrm{C}$ ) at time t=0, and the internal temperature of the potato

is greater than $27^{\circ} \mathrm{C}$ for all times t>0. The internal temperature of the potato at time t minutes can be

modeled by the function H that satisfies the differential equation $\frac{d H}{d t}=-\frac{1}{4}(H-27)$, where H(t) is

measured in degrees Celsius and H(0)=91.

For t<10, an alternate model for the internal temperature of the potato at time t minutes is the function

G that satisfies the differential equation $\frac{d G}{d t}=-(G-27)^{2 / 3}$, where G(t) is measured in degrees Celsius

and G(0)=91. Find an expression for G(t). Based on this model, what is the internal temperature of the

potato at time t=3 ?