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advanced-math

A virus spreads exponentially. On day 0, 10 people are infected. On day 3, 80 people are infected. What is the daily growth factor?

A

2

B

3

C

8

D

70

Correct Answer: A

Choice A is the correct answer. Find the growth factor per day.

  1. Formula: P(t)=P0(b)tP(t) = P_0(b)^t where P0=10P_0 = 10, P(3)=80P(3) = 80.
  2. Set up: 80=10(b)380 = 10(b)^3.
  3. Solve: b3=8b^3 = 8, so b=2b = 2.
  4. Verification: 10(2)3=10(8)=8010(2)^3 = 10(8) = 80

💡 Strategic Tip: To find base bb, isolate btb^t and take the appropriate root.

Choice B is incorrect because10(3)3=270eq8010(3)^3 = 270 eq 80. Choice C is incorrect because this is b3b^3, not bb. Choice D is incorrect because this is the difference, not the factor.