Question

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. which graph shows the temperature difference y (degrees celsius) after x seconds? choose 1 answer:

Explanation:

Step1: Identify the exponential - decay formula

The general form of an exponential - decay function is $y = a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay, and $x$ is the number of time - intervals. Here, $a = 100$ (the initial temperature difference), $r=0.6$ (60% decay rate), so the function is $y = 100(1 - 0.6)^x=100\times0.4^x$.

Step2: Analyze the initial condition

When $x = 0$, $y=100\times0.4^0 = 100$. This means the graph should start at the point $(0,100)$.

Step3: Analyze the behavior of the function

Since $0\lt0.4\lt1$, the function is a decreasing exponential function. As $x$ increases, $y$ gets closer and closer to 0 but never reaches 0.

Answer:

A. Option A (the graph that starts at the point $(0, 100)$ and is a decreasing exponential curve approaching the $x$ - axis)