[JCBreckenridge]

N (2^(x-1) = Y

X = 10 Y = 40

N (1024) = 40

N = 40/1024

N = 0.039

0.039 2^X = 10

10/0.039 = 2^x = 256

x = log 256/ log 2

x = 8

Where N = total number of days and x = original height, and Y equals the current height.

Logarithms are your friend.

X = 40 * log (N-1)/ log 2

Since we know that 10 days got us to 40 in height we have:

X = 40 * log 10 / log 2

Day 8 it is 10.

10 = 40 *

Log(base2)40 =

Log 40/
Log 2

=

ln(40) =

[Nervous Tick]

>> Day 8 it is 10.

I did it a little differently.

Tree doubles every day, so it *halves* every “yesterday”. Today (day 10) it’s 40 feet.
So yesterday (day 9) it was half that — 20 feet.
Day before that (day 8) it was half THAT — 10 feet. Done.

Not that there’s anything wrong with logarithmic math.

Sometimes test taking requires quicker stragegies though.