Problema Solution
There is an inch worm at the bottom of a 30 inch deep well. Each day the inch worm climbs up three inches then back down 2 inches.
How many day does it take the inch worm to get out of the 30 inch deep well?
Answer provided by our tutors
let 'x' be the number of days that the inch worm needs to climb out the well
the function f(x) = 1 + 3x - 2x describes the distance after x days
f(x) = 1 + x
we need to find the smallest x such that f(x) >= 30 that is
1 + x >= 30
x >= 30 - 1
x >= 29
indeed after 28 days the warm will be 28*3 - 28*2 + 1 = 29 inches distance from the bottom of the well
on the 29th day he will go 3 inches up and not go down since 29 + 3 = 32 > 30 that is he will get out of the well
the inch warm needs 29 days to get out of the well.