1
advanced-math

A streaming service grows from 1 million to 16 million subscribers in 4 years. What is the annual growth factor?

A

2

B

4

C

16

D

8

Correct Answer: A

Choice A is the correct answer. Find the annual growth factor.

  1. Formula: S(t)=S0(b)tS(t) = S_0(b)^t where S0=1S_0 = 1, S(4)=16S(4) = 16.
  2. Solve: 16=1(b)416 = 1(b)^4, so b4=16b^4 = 16.
  3. Calculate: b=164=2b = \sqrt[4]{16} = 2.
  4. Verify: 1(2)4=161(2)^4 = 16

💡 Strategic Tip: To find bb from b4=16b^4 = 16, take the 4th root.

Choice B is incorrect because this would give (4)4=256(4)^4 = 256. Choice C is incorrect because this is the total growth, not annual factor. Choice D is incorrect because this doesn't match b4=16b^4 = 16.