A rocketry club is holding a competition. There is cloud cover at 1000 ft that extends across the sky. The rocket is launched at an initial velocity of 275 ft/sec from a height of 3 feet. The function models the height of the rocket in feet, 2 seconds after the rocket is launched.

14001

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

source:  

-3(b-8)-5=9(b+2)+1

distribute

-3b+24-5=9b+18+1

add/ subtract

-3b+20=9b+19

20-19= 1

-3b+1=9b

9b+3b= 12b

1=12b

1 divided by 12 = 1/12

answer: 1/12 = b