5

Set 11: Exponential Functions (Intermediate)

Explanation

Answer: A

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

✓ Correct
B.

10,000

C.

9,000

D.

5,000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Evaluate at t=0t = 0. 1. Substitute: S(0)=100001+9e0=100001+9S(0) = \frac{10000}{1 + 9 e^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.

Key Steps:

The correct answer is 1,000

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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