Question

The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?

Answer 1

between 222 and 223 days

Explanation:

This relation includes the point (0, 2).

A proportional relation must include the point (0, 0).

This is not proportional, but it may be linear.

Points: (0, 2), (2, 20)

y = mx + b

20 = (20 - 2)/(2 - 0) × 2 + b

20 = 18/2 × 2 + b

b = 2

y = 18x + 2

When 4000 people know, y = 4000.

y = 18x + 2

4000 = 18x + 2

3998 = 18x

x = 3998/18

x = 222.111...

Answer: between 222 and 223 days