Question

Does this table represent an exponential function?

X
0
1
2
3
4
​Y
3
4.2
5.88
8.232
11.5248
A. Yes
B. No

Answer 1

The table represents an exponential function because the ratio of subsequent Y values is approximately constant, which is a characteristic of exponential growth.

Step-by-step explanation:

To determine if the presented table represents an exponential function, we must check if the ratio of Y values for consecutive X values is constant. An exponential function has the form y = ab^x, where a is the initial value, b is the base (a constant factor), and x is the exponent. Let's check the given table:

• For X=0 to X=1, the ratio is 4.2/3 = 1.4.
• For X=1 to X=2, the ratio is 5.88/4.2 ≈ 1.4.
• For X=2 to X=3, the ratio is 8.232/5.88 ≈ 1.4.
• For X=3 to X=4, the ratio is 11.5248/8.232 ≈ 1.4.

Since the ratio is approximately 1.4 for each interval of X, this suggests that the function is indeed exponential. The doubling time or growth rate is consistent, indicating exponential growth. Therefore, the answer to the question is A. Yes, this table represents an exponential function.