at the moment a hot iron rod is plunged into freezing water, the difference between the rods and the waters…

at the moment a hot iron rod is plunged into freezing water, the difference between the rods and the waters 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) =

at the moment a hot iron rod is plunged into freezing water, the difference between the rods and the waters 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) =

Answer

Explanation:

Step1: Identify the initial value

The initial temperature - difference is $a = 100$.

Step2: Identify the decay factor

The temperature - difference drops by 60% every second. So the remaining percentage of the temperature - difference each second is $100%-60%=40% = 0.4$. The decay factor $b = 0.4$.

Step3: Write the exponential - decay function

The general form of an exponential - decay function is $D(t)=a\times b^{t}$, where $a$ is the initial value and $b$ is the decay factor. Substituting $a = 100$ and $b = 0.4$ into the formula, we get $D(t)=100\times(0.4)^{t}$.

Answer:

$D(t)=100\times(0.4)^{t}$