There is an old riddle about a frog at the bottom of a 20-foot well. if he climbs up 3 feet each day and slips back 2 feet each night, how many days will it take him to reach the 20-foot mark and climb out of the well?

For this case what we are going to do is write step by step the equation of the line

f (x) = mx + b

We have:

20-foot well:

f (x) = mx + 20

if he climbs up 3 feet each day and slips back 2 feet each night:

f (x) = - 3x + 2x + 20

f (x) = - x + 20

When it reaches 20 feet we have f (x) = 0:

f (x) = - x + 20

0 = - x + 20

x = 20 days.

Answer:

It will take him 20 days to reach the 20-foot mark and climb out of the well