Question

at the moment a hot iron rod is plunged into freezing water, the difference between the rods and the waters temperatures is $100^{\circ}$ 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. $d(t) = \square$

Explanation:

Step1: Identify initial temperature difference

Initial value $D_0 = 100$

Step2: Determine remaining temperature factor

Since 60% drops, 40% remains: $1 - 0.6 = 0.4$

Step3: Formulate exponential decay function

Exponential decay formula: $D(t) = D_0 \times (remaining\ factor)^t$

Answer:

$D(t) = 100(0.4)^t$