At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50^(@) Celsius. This causes the cake to cool and the temperature difference loses (1)/(5) of its value every minute. Write a function that gives the temperature difference in degrees Celsius, D(t),t minutes after the cake was put in the cooler. D(t)=

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At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is  50^(@) Celsius. This causes the cake to cool and the temperature difference loses  (1)/(5) of its value every minute. Write a function that gives the temperature difference in degrees Celsius,  D(t),t minutes after the cake was put in the cooler.  D(t)=

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Identify Initial Difference:  Step 1: Identify the initial temperature difference and the rate at which it decreases. The initial temperature difference is 50 degrees Celsius, and it loses 1/5 of its value every minute. Determine Decay Function Form:  Step 2: Determine the form of the function that models exponential decay. The general form of an exponential decay function is D(t) = D_0 * (1 - r)^t, where D_0 is the initial value, r is the decay rate, and t is time in minutes. Plug in Values:  Step 3: Plug in the initial temperature difference and the decay rate into the exponential decay function. The initial temperature difference D_0 is 50 degrees Celsius, and the decay rate r is 1/5 or 0.2. Therefore, the function becomes D(t) = 50 * (1 - 0.2)^t. Simplify Function:  Step 4: Simplify the function. The expression (1 - 0.2) is equal to 0.8. So, the function simplifies to D(t) = 50 * 0.8^t. Write Final Function:  Step 5: Write the final function. The function that gives the temperature difference in degrees Celsius, D(t), t minutes after the cake was put in the cooler is D(t) = 50 * 0.8^t.

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