Exponents And Absence Table
1. Evaluate $2^{-4}$.
Recall that $a^{-n} = \frac{1}{a^n}$.
So, $2^{-4} = \frac{1}{2^4}$.
Calculate $2^4 = 2 \times 2 \times 2 \times 2 = 16$.
Thus, $2^{-4} = \frac{1}{16}$.
2. Create a two-way table for absences of Classes A and B for three terms: Autumn, Spring, Summer.
Given for Class A:
- Autumn term absences = 90
- Spring term absences = 120
- Summer term absences = 40
Class B absences are calculated as follows:
- Autumn: 3/10 fewer than Class A means Class B has $90 \times (1 - \frac{3}{10}) = 90 \times 0.7 = 63$ absences.
- Spring: 5% more than Class A means Class B has $120 \times (1 + 0.05) = 120 \times 1.05 = 126$ absences.
- Summer: 7 more absences than Class A means Class B has $40 + 7 = 47$ absences.
3. Complete the two-way table:
| Term | Class A Absences | Class B Absences |
|--------|------------------|------------------|
| Autumn | 90 | 63 |
| Spring | 120 | 126 |
| Summer | 40 | 47 |