00:01
So here we're thinking about compounded change, right? so at the beginning of the period, let's call that year zero, the rate of accidents was 33%.
00:11
At year one and year two, all the way down to year seven, right? seven years of change, we know that there's this constant, uniform and compounded annual rate of decrease, right? so if we think about let's call the rate is equal to x.
00:31
Year one must be, well, we started off with 0 .33, and then that's shrinking.
00:38
So let's shrink it by x, right? we are shrinking the rate by x.
00:44
And then in year two, we are starting with the value of year one and then shrinking that new value by 1 minus x, right? and so this is just 033, 1 minus x all squared.
00:58
And similarly, in year 7, we would have, well, we started at 33%.
01:03
We were shrinking it by x for seven years.
01:08
And after shrinking it by x at seven years, we ended up with 10%.
01:13
Right...