10
advanced-math

The number of hybrid cars sold follows S(t)=100001+9e1.2tS(t) = \frac{10000}{1 + 9e^{-1.2t}} where tt is years. How many are sold initially?

A

1,000

B

10,000

C

9,000

D

5,000

Correct Answer: A

Choice A is the correct answer. Evaluate at t=0t = 0.

  1. Substitute: S(0)=100001+9e0=100001+9S(0) = \frac{10000}{1 + 9e^0} = \frac{10000}{1 + 9}.
  2. Simplify: S(0)=1000010=1000S(0) = \frac{10000}{10} = 1000.
  3. Result: 1,000 cars sold initially.

💡 Strategic Tip: Initial value of logistic function: K1+A\frac{K}{1+A}.

Choice B is incorrect because this is the carrying capacity (maximum). Choice C is incorrect because this calculation is wrong. Choice D is incorrect because this would be if A=1A = 1, not A=9A = 9.