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shames · May 4, 2007, 03:59 AM

(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 ΔB is found by the formula,

ΔB=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?

Capuchin · May 4, 2007, 04:35 AM

Hi shames.

Here at AMHD, we believe that the bestway to learn is to do. If we do your homework for you, then you do not learn.

If you could start on some of these questions, then ask us specific questions when you get stuck, we can help you much better.

Good luck!

shames · May 4, 2007, 04:42 AM

Its not a homework it's a projrct and these are some of the questions I didn't know how to do pleez help the due date is on Sunday

Capuchin · May 4, 2007, 04:49 AM

Project/homework. Same thing to me.

Do you know how to approach the questions?

I'm perfectly happy to HELP you, just not happy to do all your work for you. Work with me and we will get it done.

galactus · May 4, 2007, 04:50 AM

I will help you get started with the first one.

We are given an initial amount of bacteria, 15000. When t= 2 hours it doubles to 30000.

This is the way you find the constant of proportionality, b.

$30000=15000e^{2b}$

$2=e^{2b}$

$ln(2)=2b$

Therefore, $b=\frac{ln(2)}{2}$

Now, you should be able to answer the other questions. To find out the number of bacteria after 48 hours, use t=48.

shames · May 4, 2007, 04:58 AM

I need this help because I won't find someone who has the knowledge to answer may questions if you'll help me I will be so pleezed

shames · May 4, 2007, 05:01 AM

Where will I subsitute the 48 hours

galactus · May 4, 2007, 05:03 AM

Please don't take this the wrong way, but maybe you should also work on your spelling and punctuation.

'pleezed'?

shames · May 4, 2007, 05:06 AM

Now I multiply the B with the 48

Isn't it right

galactus · May 4, 2007, 05:17 AM

Yes, you now have $y=15000e^{\frac{ln(2)}{2}t}$

Sub in t=48 to find the amount of bacteria at 48 hours.

shames · May 4, 2007, 05:24 AM

I got a very big answer

Now what about the average growth rate