1
advanced-math

A spacecraft's velocity increases by v(t)=1000e0.05tv(t) = 1000e^{0.05t} m/s where tt is seconds. What is the velocity after 20 seconds?

A

About 2,718 m/s

B

About 2,000 m/s

C

About 3,000 m/s

D

About 1,500 m/s

Correct Answer: A

Choice A is the correct answer. Evaluate at t=20t = 20.

  1. Substitute: v(20)=1000e0.05(20)=1000e1=1000ev(20) = 1000e^{0.05(20)} = 1000e^1 = 1000e.
  2. Calculate: 1000×2.718=27181000 \times 2.718 = 2718 m/s.

💡 Strategic Tip:e1=e≈2.718e^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.

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Set 39: Exponential Functions 39