5
advanced-math

Which table represents an exponential function rather than a linear function?

Table I:

xxyy
05
110
215

Table II:

xxyy
05
110
220
A

Table I only

B

Table II only

C

Both tables

D

Neither table

Correct Answer: B

Choice B is the correct answer. Check for constant differences vs constant ratios.

  1. Table I: Differences are 105=510-5=5 and 1510=515-10=5 (constant). This is linear.
  2. Table II: Ratios are 105=2\frac{10}{5}=2 and 2010=2\frac{20}{10}=2 (constant). This is exponential.
  3. Conclusion: Only Table II is exponential.

💡 Strategic Tip: Exponential functions have constant ratios between consecutive terms, while linear functions have constant differences.

Choice A is incorrect because Table I shows constant differences (linear). Choice C is incorrect because only one table is exponential. Choice D is incorrect because Table II is exponential.