1
advanced-math

A company's revenue grows from $500,000 to $4,000,000 in 6 years. What is the annual growth factor?

A

About 1.41

B

2.0

C

8.0

D

1.5

Correct Answer: A

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

  1. Total Growth: 4,000,000500,000=8\frac{4,000,000}{500,000} = 8.
  2. Formula: 4,000,000=500,000(b)64,000,000 = 500,000(b)^6, so b6=8b^6 = 8.
  3. Solve: b=86=81/6=(23)1/6=21/21.414b = \sqrt[6]{8} = 8^{1/6} = (2^3)^{1/6} = 2^{1/2} \approx 1.414.

💡 Strategic Tip: To find bb, take the 6th root of the total growth factor.

Choice B is incorrect because this would give (2)6=64(2)^6 = 64. Choice C is incorrect because this is the total growth, not annual. Choice D is incorrect because(1.5)611.39eq8(1.5)^6 \approx 11.39 eq 8.