the amount of water in a tank can be modeled by the function w(t). which expression would indicate that the…

the amount of water in a tank can be modeled by the function w(t). which expression would indicate that the amount of water in the tank is decreasing? w(t) > 0 w(t) < 0 w(t) > 0 w(t) < 0

the amount of water in a tank can be modeled by the function w(t). which expression would indicate that the amount of water in the tank is decreasing? w(t) > 0 w(t) < 0 w(t) > 0 w(t) < 0

Answer

Answer:

$W'(t)<0$

Explanation:

Step1: Recall derivative meaning

The first - derivative $W'(t)$ of a function $W(t)$ represents the rate of change of the function $W(t)$ with respect to $t$.

Step2: Analyze decreasing condition

If a function $y = f(x)$ is decreasing, then its derivative $f'(x)<0$. Here, $W(t)$ represents the amount of water in the tank and $t$ is time. So, when the amount of water in the tank is decreasing, the rate of change of the amount of water with respect to time, $W'(t)<0$.

Step3: Analyze second - derivative

The second - derivative $W''(t)$ represents the rate of change of the first - derivative $W'(t)$. $W''(t)>0$ means $W'(t)$ is increasing and $W''(t)<0$ means $W'(t)$ is decreasing, which is not relevant to the function $W(t)$ being decreasing.