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Let's break down the questions from the image and solve them.

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### Question 2: Balloon Surface Area as a Function of Volume

Given:
- \( V \) represents the volume of air in the balloon (in cm³).
- \( S \) represents the surface area of the balloon (in cm²).
- The function \( f(V) = S \), which expresses surface area \( S \) as a function of volume \( V \).

#### (a) Explain the meaning of \( f(4) \) in this context.
- **Solution:**
  The expression \( f(4) \) refers to the surface area of the balloon when the volume of air inside the balloon is 4 cm³. In other words, \( f(4) = S \) gives the surface area when \( V = 4 \).

#### (b) Explain the meaning of \( f(V) = 11.3 \) in this context.
- **Solution:**
  The equation \( f(V) = 11.3 \) means that when the volume of air inside the balloon is \( V \), the surface area of the balloon is 11.3 cm². It indicates that at some specific volume \( V \), the balloon’s surface area reaches 11.3 cm².

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### Question 3: Wilting Rose Height as a Function of Time

Given:
- The function \( g(t) = 8.65 - 1.3t \) models the height of the rose (in inches), where \( g(t) \) gives the height after \( t \) days since the rose began wilting.

#### (a) Compute the value of \( g(5) \) and explain the meaning in this context.
- **Solution:**
  \[
  g(5) = 8.65 - 1.3(5) = 8.65 - 6.5 = 2.15
  \]
  The value \( g(5) = 2.15 \) means that 5 days after the rose began wilting, its height is 2.15 inches.

#### (b) Compute the value of \( t \) for which \( g(t) = 5 \) and explain the meaning in this context.
- **Solution:**
  To find \( t \), solve \( g(t) = 5 \):
  \[
  5 = 8.65 - 1.3t
  \]
  Rearranging the equation:
  \[
  1.3t = 8.65 - 5
  \]
  \[
  1.3t = 3.65
  \]
  \[
  t = \frac{3.65}{1.3} \approx 2.81
  \]
  So, \( t \approx 2.81 \). This means that approximately 2.81 days after the rose began wilting, its height was 5 inches.

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Would you like more details on any part of the solutions? Here are some related questions for practice:

1. What would \( f(V) \) look like for a spherical balloon in terms of \( V \)?
2. If the volume doubles, what happens to the surface area of the balloon assuming it's spherical?
3. How would you interpret \( g(0) \) in the rose wilting problem?
4. What happens to the height of the rose after 10 days?
5. How can we model the total volume of air inside a balloon as a function of its surface area?

**Tip:** When solving word problems, always try to connect the mathematical model back to the real-world scenario.

2. The surface area of a balloon increases as the volume of air inside the balloon increases. Let V represent the volume of air in the balloon (in cm³), and let S represent the surface area of the balloon (in cm²). Define the function f by f(V) = S. (a) Explain the meaning of f(4) in this context. (b) Explain the meaning of f(V) = 11.3 in this context. 3. A rose is wilting, causing the height of the plant to decrease at a constant rate of change. The function g(t) = 8.65 - 1.3t where g(t) = h models the height of the rose (in inches), denoted h, in terms of the time since the rose began wilting (in days), denoted t. (a) Compute the value of g(5) and explain the meaning in this context. (b) Compute the value of t for which g(t) = 5 and explain the meaning in this context.

Learn how to interpret the surface area of a balloon based on its volume and how a wilting rose's height decreases over time using functions. This problem focuses on function evaluation, real-world interpretation of function values, and solving linear equations.

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