A dolphin eats 30 pounds of fish per day.

a. Write and graph a function that relates the number p of pounds of fish that a dolphin eats in d days.
b. How many pounds of fish does a dolphin eat in 30 days?

1 answer

Sure! Let's tackle each part step by step.

### Part a: Writing and graphing the function

1. **Writing the function:**

The function that relates the number \( p \) of pounds of fish that a dolphin eats in \( d \) days can be written as:

\[
p(d) = 30d
\]

Here, \( p(d) \) represents the total pounds of fish, and \( d \) represents the number of days.

2. **Graphing the function:**

To graph this function, you plot \( p \) on the vertical (y) axis and \( d \) on the horizontal (x) axis.

- When \( d = 0 \), \( p(0) = 30 \times 0 = 0 \)
- When \( d = 1 \), \( p(1) = 30 \times 1 = 30 \)
- When \( d = 2 \), \( p(2) = 30 \times 2 = 60 \)
- When \( d = 3 \), \( p(3) = 30 \times 3 = 90 \)

And so on. This linear relationship will form a straight line passing through the origin.

#### Plotting Points:
| \( d \) (days) | \( p(d) \) (pounds) |
|:--------------:|:-------------------:|
| 0 | 0 |
| 1 | 30 |
| 2 | 60 |
| 3 | 90 |
| 4 | 120 |

### Part b: Calculating pounds of fish in 30 days

To find out how many pounds of fish a dolphin eats in 30 days, substitute \( d = 30 \) into the function:

\[
p(30) = 30 \times 30 = 900
\]

So, a dolphin eats **900 pounds of fish in 30 days**.