1. The amount of bacteria found in hospital operating rooms is inversely proport
ID: 2847735 • Letter: 1
Question
1. The amount of bacteria found in hospital operating rooms is inversely proportional to the square of the strength of the sanitizer used to clean the room. If there are 100 million bacteria after a cleaning with a sanitizer of strength 25, how many bacteria, in millions to the nearest million, would be present if the operating room were cleaned with a sanitizer of strength 35?
2. Each year the thickness of Antarctic ice varies between 2400m on July 15 and 1400m on January 15.
a. Find a possible model (formula) for the depth of the ice as a function of t in months.
b. What is the thickness, to the nearest meter, of the ice on May 15?
3. In 1977 NASA launched the Voyager spacecraft. Voyager carries sample images and sounds from earth with the idea to announce the presence of intelligent life on earth to whoever might encounter it in deep space. Voyager is powered by Plutonium-238, which has a half-life of 96 years. When the original amount of Plutonium-238 reaches 2.5% of its original amount, the spacecraft will power down. In what year will this power down occur? Round intermediate results to 5 decimal places.
Explanation / Answer
1. number of bacteria is inversely proportional to the ( strength of sanitizer)^2
number of bacteria in case 1 = 100 million when strength of sanitizer is 25
now strength of sanitizer is 35
number of bacteria in case 1 / number of bacteria in case 2 = 35^2 / 25^2 ( due to invere proportionality)
number of bacteria in case 2 = 100*625/ 35^2 = 51 million
2. July 15 it is 2400 , january 15 it is 1400
considering months it is 6 months
it is also increasing
y = depth of the ice
y = 1400 + 167*t where t is in months 0< t <6
b) on may 15 , y = 1400 + 4*167 = 2068
3. half life = 96 years
N(t) = (1/2)*N(0) when t = 96 ==> N(96) = 1/2*N(0) ; N(192) = 1/2* ( 1/2*N(0)) = 1/4*N(0)
when N(t) = (0.025)*N(0) at that valueof t space craft will power down.
N(k*96) = (1/2^k)*N(0)
for 1/2^k = 0.025 ==> 2^k = 1000/25 = 40 ==> k = log(40)/ log(2) = 5.321928
so it takes 96*k years ==> 511 years
So it takes 511 years to stop working
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