Set 11: Exponential Functions

Explanation

Answer: A

A spacecraft's velocity increases by $v(t) = 1000e^{0.05t}$ m/s where $t$ is seconds. What is the velocity after 20 seconds?

About 2,718 m/s

✓ Correct

About 2,000 m/s

About 3,000 m/s

About 1,500 m/s

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Evaluate at $t = 20$ . 1. Substitute: $v(20) = 1000 e^{0.05(20)} = 1000 e^1 = 1000 e$ . 2. Calculate: $1000\times 2.718 = 2718$ m/s. Strategic Tip: $e^1 = e \approx 2.718$ . Choice B is incorrect because this assumes linear growth. Choice C is incorrect because this overestimates the growth. Choice D is incorrect because this is too low.

Key Steps:

•

The correct answer is About 2,718 m/s

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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