8

Set 2: Exponential Functions

Explanation

Answer: B

The number of bacteria in a culture is given by N(t)=2000(3)tN(t) = 2000(3)^t, where tt is in hours. What is the initial number of bacteria?

Bacterial Growth

A.

3

B.

2000

✓ Correct
C.

6000

D.

2003

Detailed Explanation

Choice B is correct. Choice B is the correct answer. The initial value is the coefficient aa. 1. Identify: In N(t)=abtN(t) = ab^t, aa is the starting amount. 2. Locate: a=2000a = 2000. 3. Verify: At t=0t=0, N(0)=2000(3)0=2000N(0) = 2000(3)^0 = 2000. Strategic Tip: The number in front of the parenthesis is your starting point. Choice A is incorrect because 3 is the growth factor (tripling). Choice C is incorrect because 6000 is the amount after 1 hour. Choice D is incorrect because it adds the parameters.

Key Steps:

The correct answer is 2000

Why others are wrong:
A: Choice A 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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