Set 10: Exponential Functions (Intermediate)

Explanation

Answer: A

Identify the equation for the graph passing through $(0, 2)$ and $(1, 10)$ .

$Exponential Function$

$y = 2(5)^x$

✓ Correct

$y = 5(2)^x$

$y = 2(10)^x$

$y = 2 + 8x$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find $a$ and $b$ . 1. Find a: Y-intercept is 2, so $a=2$ . 2. Find b: $y$ goes from 2 to 10. $2\times b = 10 \implies b=5$ . 3. Equation: $y = 2(5)^x$ . Strategic Tip: $b = y_2 / y_1$ when $\Delta x = 1$ . Choice B is incorrect because it swaps $a$ and $b$ . Choice D is incorrect because it is linear.

Key Steps:

•

The correct answer is $y = 2(5)^x$

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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