### Part A: Determine the test average for your math class after completing test 2.
To find the average score for the math class after completing test 2, we use the formula given by the function [tex]\( f(x) = 0.2x + 79 \)[/tex], where [tex]\( x \)[/tex] represents the number of tests taken.
For test 2:
[tex]\[ f(2) = 0.2 \times 2 + 79 \][/tex]
[tex]\[ f(2) = 0.4 + 79 \][/tex]
[tex]\[ f(2) = 79.4 \][/tex]
So, the average score for the math class after completing test 2 is 79.4.
### Part B: Determine the test average for your science class after completing test 2.
From the provided table:
For test 2 in the science class:
[tex]\[ g(2) = 84 \][/tex]
So, the average score for the science class after completing test 2 is 84.
### Part C: Which class had a higher average after completing test 4?
#### Step 1: Determine the average for the math class after test 4.
Using the function [tex]\( f(x) = 0.2x + 79 \)[/tex] for the math class:
[tex]\[ f(4) = 0.2 \times 4 + 79 \][/tex]
[tex]\[ f(4) = 0.8 + 79 \][/tex]
[tex]\[ f(4) = 79.8 \][/tex]
So, the average score for the math class after completing test 4 is 79.8.
#### Step 2: Determine the average for the science class after test 4.
The given table provides average scores for tests 1, 2, and 3 in the science class:
- [tex]\( g(1) = 86 \)[/tex]
- [tex]\( g(2) = 84 \)[/tex]
- [tex]\( g(3) = 82 \)[/tex]
We can observe a linear trend where the average decreases by 2 points after each test:
[tex]\[ g(2) - g(1) = 84 - 86 = -2 \][/tex]
[tex]\[ g(3) - g(2) = 82 - 84 = -2 \][/tex]
Assuming this trend continues, for test 4:
[tex]\[ g(4) = g(3) - 2 \][/tex]
[tex]\[ g(4) = 82 - 2 \][/tex]
[tex]\[ g(4) = 80 \][/tex]
So, the average score for the science class after completing test 4 is 80.
#### Conclusion:
- The average score for the math class after test 4 is 79.8.
- The average score for the science class after test 4 is 80.
Thus, the science class had a higher average after completing test 4.
