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A boat has a large tank of fresh water.
The tank is cylindrical and has height 
 m.
Water from the tank is used so that the water level drops by 0.1 m per day.

What function expression 
 shows the height of the water in the tank after 
 24 hours.

To model the height of the water in the tank after 24 hours, we need to establish a relationship between the height of the water and time.

Let's define the variables:

- Let \( h(t) \) represent the height of the water in the tank at time \( t \), where \( t \) is measured in days.
- The initial height of the water is \( h_0 \), which is the height of the tank (since the problem does not specify otherwise, we'll assume the tank starts full).
- The water level drops by \( 0.1 \) meters per day.

Given that the water level drops at a constant rate of \( 0.1 \) meters per day, we can express the height of the water as a function of time \( t \):

\[
h(t) = h_0 - 0.1t
\]

Now, let's substitute \( t = 1 \) day (since 24 hours equals 1 day) into the equation:

\[
h(1) = h_0 - 0.1 \times 1 = h_0 - 0.1
\]

Thus, the height of the water after 24 hours will be \( h_0 - 0.1 \) meters, where \( h_0 \) is the initial height of the water.

**Summary of the function:**

\[
h(t) = h_0 - 0.1t
\]

**After 24 hours:**

\[
h(1) = h_0 - 0.1 \, \text{meters}
\]

This function describes how the height of the water decreases linearly over time.

Would you like more details or have any questions?

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**Further related questions:**

1. What is the height of the water after 3 days?
2. How much total water is used after 5 days?
3. How would the function change if the water level dropped by 0.2 meters per day?
4. How long will it take for the tank to be empty if the water level drops at 0.1 meters per day?
5. If the tank starts at a height of 2 meters, what will the height of the water be after 10 days?

**Tip:** When solving similar problems, always identify the rate of change and establish a relationship between the variables involved to model the situation effectively.

Discover how to calculate the height of water in a cylindrical tank after 24 hours with a linear function. This problem involves understanding linear functions and rate of change. Suitable for Grades 9-12.

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