To determine the rate of change, we need to consider how the cost changes as the number of goldfish increases. We are given the following points:
| Number of Goldfish | Cost |
|--------------------|--------|
| 5 | [tex]$1.50 |
| 10 | $[/tex]3.00 |
| 15 | [tex]$4.50 |
| 20 | $[/tex]6.00 |
Since the relationship is linear, the rate of change, or slope, is constant and can be found using any two points from the table.
1. Let's examine the cost change from 5 goldfish to 10 goldfish:
- At 5 goldfish, the cost is [tex]$1.50.
- At 10 goldfish, the cost is $[/tex]3.00.
- The change in cost is [tex]$3.00 - $[/tex]1.50 = [tex]$1.50.
- The change in the number of goldfish is 10 - 5 = 5.
- Rate of change = $[/tex]\frac{\Delta \text{Cost}}{\Delta \text{Number of Goldfish}} = \frac{1.50}{5} = 0.30[tex]$ dollars per goldfish.
We can confirm this with additional calculations using other intervals, but since we know the relationship is linear, the rate of change stays consistent.
2. To verify, let's consider the cost change from 10 goldfish to 15 goldfish:
- At 10 goldfish, the cost is $[/tex]3.00.
- At 15 goldfish, the cost is [tex]$4.50.
- The change in cost is $[/tex]4.50 - [tex]$3.00 = $[/tex]1.50.
- The change in the number of goldfish is 15 - 10 = 5.
- Rate of change = [tex]$\frac{\Delta \text{Cost}}{\Delta \text{Number of Goldfish}} = \frac{1.50}{5} = 0.30$[/tex] dollars per goldfish.
Thus, the cost increases by [tex]$0.30 each time 1 goldfish is added. This verifies that the rate of change is indeed $[/tex]0.30 per goldfish.
Therefore, the correct statement describing the rate of change is:
(A) The cost increases $0.30 each time 1 goldfish is added.
