A company is testing a product which is intended to make hair grow faster. One of the test subjects started with a hair length of 8.2 inches. After a year of using the product, the test subject's hair measured 18.4 inches.

Question

If the growth rate was constant during the trial period, which of the following statements applies?
A.
An additional month of product use is associated with an additional 2.22 inches of growth.
B.
An additional month of product use is associated with an additional 0.85 inch of growth.
C.
An additional 0.85 month of product use is associated with an additional inch of growth.
D.
An additional 2.22 months of product use is associated with an additional inch of growth.

Answer 1

To determine which statement applies based on the hair growth data provided, we first need to calculate the total growth in hair length over the trial period.

1. Initial hair length: 8.2 inches
2. Final hair length: 18.4 inches

Total growth = Final hair length - Initial hair length
Total growth = 18.4 inches - 8.2 inches = 10.2 inches

Duration of the trial period: 1 year = 12 months

Average growth per month = Total growth / Number of months
Average growth per month = 10.2 inches / 12 months = 0.85 inches per month

Now we can analyze the statements:

A. An additional month of product use is associated with an additional 2.22 inches of growth.
False (growth is 0.85 inches per month)

B. An additional month of product use is associated with an additional 0.85 inch of growth.
True (this matches our calculation)

C. An additional 0.85 month of product use is associated with an additional inch of growth.
False (0.85 month would yield 0.85 * 0.85 = 0.7225 inch, not 1 inch)

D. An additional 2.22 months of product use is associated with an additional inch of growth.
False (2.22 months would give roughly 1.885 inches of growth, not exactly 1 inch)

The correct answer is: B. An additional month of product use is associated with an additional 0.85 inch of growth.