Question

The approximate number of zombies in a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential. Number of Hours Since Zombies First Spotted, x 1 2 3 4 Approx. Number of Zombies, f(x) 33 50 67 85 Answer function would best fit the data because as x increases, the y values change . Rounded to the nearest .5, the of this function is approximately

Answer 1

To determine whether the data represents a linear or exponential function, let’s analyze the changes in the number of zombies over time based on the given values.

Here is the data provided:

| Hours (x) | Number of Zombies (f(x)) |
|-----------|---------------------------|
| 1 | 33 |
| 2 | 50 |
| 3 | 67 |
| 4 | 85 |

**Step 1: Check for linearity**

To see if the data follows a linear trend, we can calculate the differences between consecutive values of \( f(x) \):

- From \( x = 1 \) to \( x = 2 \):
\( 50 - 33 = 17 \)

- From \( x = 2 \) to \( x = 3 \):
\( 67 - 50 = 17 \)

- From \( x = 3 \) to \( x = 4 \):
\( 85 - 67 = 18 \)

While the differences are close (17, 17, and 18), they are not consistent, which suggests it is not a perfect linear function.

**Step 2: Check for exponential growth**

An exponential function would show a multiplicative rate of growth rather than additive. To see if there is a percentage increase:

1. From \( x = 1 \) to \( x = 2 \):
\((50 - 33) / 33 \approx 0.515 \) or about 51.5%

2. From \( x = 2 \) to \( x = 3 \):
\((67 - 50) / 50 \approx 0.34 \) or about 34%

3. From \( x = 3 \) to \( x = 4 \):
\((85 - 67) / 67 \approx 0.269 \) or about 26.9%

The percentage changes also show a decrease, which isn't characteristic of exponential growth.

**Conclusion:**

Since the differences in the number of zombies are not consistent, we cannot classify the data perfectly as linear, but since the changes are relatively steady and could resemble a linear relationship for this small dataset, we might consider it approximately linear in this context.

To summarize:

- The data suggests a linear format because of the incremental increases being relatively uniform (though not exactly consistent).
- Thus, it is reasonable to say that a linear function best fits the data.

**Final Answer:**

A linear function would best fit the data because as \( x \) increases, the \( y \) values change in a quasi-consistent manner. Rounded to the nearest .5, the slope (the average change) of this function is approximately \( 17 \) zombies per hour at first glance, or \( \textit{(approximately 17)} \) when averaged out.