Questions: The figure to the right shows a container that is to be filled with water from the top. Assume that water is poured into the container at a constant rate and the container is filled in 10 s. Assume also that the horizontal cross sections of the container are always circles. Let h(t) be the depth of the water in the container at time t, for 0 ≤ t ≤ 10. Complete parts (a) through (d) below. b. Explain why h is an increasing function. Choose the correct answer below. A. The value of t is always increasing. B. The derivative of h is always increasing. C. Water is being added to the container at all times. D. The height of the container is increasing at all times.

The figure to the right shows a container that is to be filled with water from the top. Assume that water is poured into the container at a constant rate and the container is filled in 10 s. Assume also that the horizontal cross sections of the container are always circles. Let h(t) be the depth of the water in the container at time t, for 0 ≤ t ≤ 10. Complete parts (a) through (d) below.

b. Explain why h is an increasing function. Choose the correct answer below.
A. The value of t is always increasing.
B. The derivative of h is always increasing.
C. Water is being added to the container at all times.
D. The height of the container is increasing at all times.

Transcript text: The figure to the right shows a container that is to be filled with water from the top. Assume that water is poured into the container at a constant rate and the container is filled in 10 s . Assume also that the horizontal cross sections of the container are always circles. Let $h(t)$ be the depth of the water in the container at time $t$, for $0 \leq \mathrm{t} \leq 10$. Complete parts (a) through (d) below. b. Explain why h is an increasing function. Choose the correct answer below. A. The value of $t$ is always increasing. B. The derivative of $h$ is always increasing. C. Water is being added to the container at all times. D. The height of the container is increasing at all times.

Solution

Solution Steps

Step 1: Understanding the Problem

The problem involves a container being filled with water at a constant rate. The container has a specific shape, and we need to analyze the height of the water (h) as a function of time (t).

Step 2: Analyzing the Container Shape

The container is shaped like an inverted cone. As water is poured in, the height of the water increases. The horizontal cross-sections of the container are always circles.

Step 3: Identifying the Increasing Function

We need to explain why the height of the water (h) is an increasing function of time (t). Given that water is being added at a constant rate, the height of the water will continuously increase.