1. Problem statement: We are asked to find a function $D(t)$ that describes the temperature difference between a hot cake and the cooler after $t$ minutes. 2. Given: Initial temperature difference $D(0) = 50$°C. 3. The temperature difference decreases by \frac{1}{5} of its value per minute, meaning it retains \frac{4}{5} of its value every minute. 4. This situation describes exponential decay, where the temperature difference after $t$ minutes is given by: $$ D(t) = D(0) \times \left(\frac{4}{5}\right)^t $$ 5. Substitute the initial value: $$ D(t) = 50 \times \left(\frac{4}{5}\right)^t $$ 6. Therefore, the function that gives the temperature difference $t$ minutes after putting the cake in the cooler is: $$ D(t) = 50 \times \left(\frac{4}{5}\right)^t $$ This function decreases exponentially as $t$ increases, showing the cooling effect over time.