Question

tables of values for two different functions are given below

x	y		x	y
2	16		2	16
3	36		3	64
4	64		4	256
5	100		5	1,024
6	144		6	4,096

which statement is true?

• the right function grows approximately 21 times faster than the left function over the interval 4 < x < 5.
• the right function grows approximately 21 times slower than the left function over the interval 4 < x < 5.
• the right function grows approximately 6 times faster than the left function over the interval 2 < x < 3.
• the right function grows approximately 2.5 times slower than the left function over the interval 2 < x < 3.

Explanation:

Step1: Analyze left function (4 < x < 5)

Left function: At x=4, y=64; x=5, y=100. Growth: \( 100 - 64 = 36 \)

Step2: Analyze right function (4 < x < 5)

Right function: At x=4, y=256; x=5, y=1024. Growth: \( 1024 - 256 = 768 \)

Step3: Compare growth rates (4 < x < 5)

Ratio: \( \frac{768}{36} \approx 21.33 \), so right grows ~21x faster.

Step4: Check 2 < x < 3 (optional, confirm)

Left: x=2 (16) to x=3 (36). Growth: \( 36 - 16 = 20 \)
Right: x=2 (16) to x=3 (64). Growth: \( 64 - 16 = 48 \)
Ratio: \( \frac{48}{20} = 2.4 \), not 6 or 2.5 slower. So first option holds.

Answer:

The right function grows approximately 21 times faster than the left function over the interval \( 4 < x < 5 \).