Let's solve the question step by step.
### Part (a)
We need to determine how many times more memory pen drive D has compared to pen drive B.
1. For pen drive B, the memory capacity is [tex]\(2^2\)[/tex] GB.
2. For pen drive D, the memory capacity is [tex]\(2^4\)[/tex] GB.
To find how many times more memory pen drive D has compared to pen drive B, we divide the memory of pen drive D by the memory of pen drive B.
So,
[tex]\[ \text{Times more memory} = \frac{\text{Memory of pen drive D}}{\text{Memory of pen drive B}} = \frac{2^4}{2^2} = \frac{16}{4} = 4 \][/tex]
Therefore, pen drive D has 4 times more memory than pen drive B.
### Part (b)
To determine if memory and price are directly proportional, we need to calculate the price per memory unit for each pen drive and check if these ratios are consistent across all pen drives.
1. For pen drive A:
[tex]\[ \text{Price per memory unit} = \frac{400}{2^1} = \frac{400}{2} = 200 \][/tex]
2. For pen drive B:
[tex]\[ \text{Price per memory unit} = \frac{600}{2^2} = \frac{600}{4} = 150 \][/tex]
3. For pen drive C:
[tex]\[ \text{Price per memory unit} = \frac{800}{2^3} = \frac{800}{8} = 100 \][/tex]
4. For pen drive D:
[tex]\[ \text{Price per memory unit} = \frac{1000}{2^4} = \frac{1000}{16} = 62.5 \][/tex]
To be directly proportional, all these ratios would need to be equal. As we can see, the ratios are:
- 200 for pen drive A
- 150 for pen drive B
- 100 for pen drive C
- 62.5 for pen drive D
Since these ratios are not equal, the memory and price are not directly proportional.
### Answer Summary:
(a) Pen drive D has 4 times more memory than pen drive B.
(b) Memory and price are not directly proportional to each other.
