Set 10: Exponential Functions (Intermediate)

Explanation

Answer: A

The table shows data from two functions:

$x$	$f(x)$	$g(x)$
0	10	10
1	20	15
2	40	20

Which statement is true?

$f(x)$ is exponential, $g(x)$ is linear

✓ Correct

$f(x)$ is linear, $g(x)$ is exponential

Both are exponential

Both are linear

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check ratios and differences. 1. $f(x)$ : Ratios $\frac{20}{10}=2$ , $\frac{40}{20}=2$ → Exponential (base 2). 2. $g(x)$ : Differences $15 -10=5$ , $20 -15=5$ → Linear (slope 5). 3. Conclusion: $f(x)$ is exponential, $g(x)$ is linear. Strategic Tip: Constant ratios = exponential. Constant differences = linear. Choice B is incorrect because it reverses the classifications. Choice C is incorrect because $g(x)$ has constant differences. Choice D is incorrect because $f(x)$ has constant ratios.

Key Steps:

•

The correct answer is $f(x)$ is exponential, $g(x)$ is linear

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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Set 10: Exponential Functions (Intermediate)

Detailed Explanation

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