2
advanced-math

A population of bacteria is modeled by the function P(t)=500(0.85)tP(t) = 500(0.85)^t, where tt is time in hours. What is the decay factor?

A

500

B

0.85

C

0.15

D

15

Correct Answer: B

Choice B is the correct answer. The decay factor is the base of the exponent.

  1. Identify: In the form y=abxy = ab^x, the base bb represents the growth or decay factor.
  2. Locate: In P(t)=500(0.85)tP(t) = 500(0.85)^t, the base is 0.85.
  3. Interpret: Since 0<0.85<10 < 0.85 < 1, it represents decay, and 0.85 is the decay factor.

💡 Strategic Tip: The factor bb is what you multiply by each step. If b<1b < 1, the quantity decreases.

Choice A is incorrect because 500 is the initial population. Choice C is incorrect because 0.15 represents the decay rate (1−0.85=0.151 - 0.85 = 0.15 or 15%), not the factor. Choice D is incorrect because 15 is the percentage rate, not the factor.