Question

Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.

Answer 1

Second table

The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16

Explanation:

y = 2^x

2 = 2¹

4 = 2²

8 = 2³

16 = 2⁴

Answer 2

Table 2

Explanation:

We have the tables:

Table 1:

x: 1 2 3 4

y: 2 4 6 8

Table 2:

x: 1 2 3 4

y: 2 4 8 16

Table 3:

x: 1 2 3 4

y: 2 4 7 11

Table 4:

x: 1 2 3 4

y: 2 4 6 10

An exponential growth data set will show a common ratio between y values. Let's look at each of the ratios from each table.

Table 1:

8/6 = 4/3

6/4 = 3/2

Already, we can see that 4/3 ≠ 3/2, which means that this doesn't have a common ratio. So Table 1 is wrong.

Table 2:

16/8 = 2

8/4 = 2

4/2 = 2

The common ratio here is 2, so we know this is correct.

Table 3:

11/7 = 1.57

7/4 = 1.75

Again, we can see that 1/57 ≠ 1.75, so this is wrong.

Table 4:

10/6 = 1.67

6/4 = 1.5

Again, there is no common ratio here, so this is wrong.

The answer is thus Table 2.