At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is 100^(@) Celsius. This causes the iron to cool and the temperature difference drops by 60% every second. Write a function that gives the temperature difference in degrees Celsius, D(t),t seconds after the rod was plunged into the water. D(t)=

Question

At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is  100^(@) Celsius. This causes the iron to cool and the temperature difference drops by  60% every second. Write a function that gives the temperature difference in degrees Celsius,  D(t),t seconds after the rod was plunged into the water.  D(t)=

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Identify Initial Temperature Difference:  Step 1: Identify the initial temperature difference when the iron rod is plunged into the water. The problem states that the initial temperature difference is 100 degrees Celsius. This is the value of D(0), the temperature difference at time t = 0 seconds. Determine Rate of Decrease:  Step 2: Determine the rate at which the temperature difference decreases. The problem states that the temperature difference drops by 60% every second. This means that each second, the temperature difference is 40% (100% - 60%) of what it was the previous second. Express Rate as Decimal:  Step 3: Express the rate of decrease as a decimal to be used in the exponential decay function. The rate of 40% as a decimal is 0.40. Write Exponential Decay Function:  Step 4: Write the exponential decay function. The general form of an exponential decay function is D(t) = D(0) * (decay factor)^(t), where D(0) is the initial amount, decay factor is the percentage of the amount remaining after each time interval, and t is the time in seconds. Substitute Known Values:  Step 5: Substitute the known values into the exponential decay function. The initial temperature difference is D(0) = 100 degrees Celsius, and the decay factor is 0.40. Therefore, the function is D(t) = 100 * 0.40^(t). Simplify Function:  Step 6: Simplify the function if necessary. In this case, the function is already in its simplest form, so no further simplification is needed.

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