Let's analyze the given problem step by step:

Part A: The Antarctic ice sheet loss rate in 2010

To determine the rate of ice loss (slope), we use the two given points:

• $(5, 5)$ and $(10, -240)$.

The slope $m$ of the line is calculated using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the values:
$m = \frac{-240 - 5}{10 - 5} = \frac{-245}{5} = -49$

Thus, the Antarctic ice sheet was losing ice at a rate of 49 gigatons per year in 2010.

Part B: Decrease in ice volume from 2010 to 2015

From the graph:

• At $t = 10$ (2010), $V(10) = -240$
• At $t = 15$ (2015), $V(15) = -160$.

The decrease in ice volume is:
$\text{Change in volume} = V(15) - V(10) = -160 - (-240) = -160 + 240 = 80$

Thus, the Antarctic ice sheet decreased by 80 gigatons from 2010 to 2015.

Part C: Decrease in ice volume from 2000 to 2024

We calculate the total change in ice volume from $t = 0$ (2000) to $t = 24$ (2024):

• At $t = 0$, $V(0) = 5$
• At $t = 24$, $V(24) = -110$.

The total change in volume is:
$\text{Change in volume} = V(24) - V(0) = -110 - 5 = -115$

Thus, the Antarctic ice sheet decreased by 120 gigatons (rounded to the tens position).

Summary of Answers:

1. Part A: Rate of loss = 49 gigatons per year
2. Part B: Decrease = 80 gigatons
3. Part C: Total decrease = 120 gigatons

Do you need further clarification or detailed steps? Let me know! Here are 5 follow-up questions to expand on the topic:

1. How do you interpret the slope of a line in a real-world context like this graph?
2. What does a positive or negative slope indicate in terms of ice volume change?
3. Can you calculate the rate of change from $(15, -160)$ to $(24, -110)$?
4. How do you find the equation of a line given two points on the graph?
5. How does a piecewise function help describe the changes in ice volume over time?

Tip: The slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ is crucial for understanding changes over time in linear data!