Expert: Sherman D. - 5/4/2007

Question
please listen this is a project and i solved arond 10 pages and these are the questions i faced some problem solving so please help me i need your knowledge

(Q#2) A certain type of primitive bacteria was  recently discovered in a rock sample from a meteor shower. The original count was 15000 bacteria. Placed in a nutrient rich rich environment in a government research lab in Burbank, California, the bacteria began to grow rapidly. Two hours later, the number of bacteria had doubled, that is, there were 30000 bacteria in the culture. Effort to slow the growth of the bacteria failed and after two days the entire lab was tangled mass of weird, pulsating alien slime. Use the exponential growth model ( y=ae^(bt) ) B>0.

1)   find an equation that represents the number of bacteria ( t ) hours after the original count of 15000.
2)   Find the amount of bacteria present after 48 hours.
3)   What is the average growth rate?


(Q#3) Logarithmic scales: (sounds fishy to me!) if you study some of the results from experimental psychology, it turns out that human senses such as sight and hearing operate on a logarithmic scale. (true fact !) for example, suppose you are staring at a light bulb that gives off light measure at a certain intensity ( I ). Someone turns the switch and suddenly the light intensity emitted by the bulb is twice as much as the first intensity. What do you perceive has happened? That is, does the light look twice as bright? No! to the average person, it only looks on the order of (log2 times I)as bright! Our “visual information processing” system changes (transduces) the incoming light signals.  

1)   if you double the intensity of the light bulb, that is, increase it to 2 x I, what does the average person perceive (roughly speaking) has happened? (how much brighter does the light bulb look? )
2)   since perception brightness is logarithmic, would you say that we tend to see lighted objects brighter than they really are, or not as bright?


(Q#4) (Refer back to #3 above.) suppose that the person viewing the light is a vampire. Lets say that to a vampire, perceived light intensity looks different than it does to us mortals. Vampires allegedly having keen eyesight (and hearing as well), let us say that the vampires perception works exponentially rather than logarithmically. That is, when you turn up the lights from intensity (I#1) to intensity (I#2), the change is perceived brightness ÄB is found by the formula,

           
ÄB=ke^(I#2/I#1)

1)   what happens when the actual light intensity is doubled? By how much is perceived brightness magnified?
2)   What about when the actual light intensity is three times greater? By how much is the perceived brightness magnified?
3)   Since the vampire perception of light is (according to our light of fancy here) exponential, would you say that he tends to see lighted objects brighter than they really are, or not as bright?


Answer
Q2.)
1) find an equation that represents the number of bacteria ( t ) hours after the original count of 15000.

y = 15000e^(bt)

2 = e^(b(2))
2 = (e^b)^2
sqrt(2) = e^b
ln(sqrt(2)) = b
b = (1/2)ln(2) or (ln(2)/2)

y = 15000e^((t/2)ln(2))
y = 15000(e^(ln(2)))^(t/2)
y = 15000 * 2^(t/2)

Thats an easier way to put it. So depending on how you want the formula to look like

ANS : y = 15000e^((t/2)ln(2)) or y = 15000 * 2^(t/2)

by the way, if you are wondering why i put it as 2 = e^(2b)

its because if you do 30000 = 15000e^(2b), then divide both sides by 15000, you will get 2 = e^(2b)

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2) Find the amount of bacteria present after 48 hours.
y = 15000 * 2^(48/2)
y = 15000 * 2^24
y = 15000 * 16777216
y = 251658240000

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3) What is the average growth rate? about 34.657%

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Q3 and Q4. Sorry, i can't help you on this one. Check with answers.yahoo.com

on Q4. #3, the answer is Brighter than they really are. If you are wondering how do i know. Its because i've seen a bunch of Vampire movies to know that.