I Do Not Understand How To Solve This... Please Help

[TheWiseBoy]

Ernie has been watching an earthquake building near Irvine, California. Earthquakes that measure more than 5 on the Richter Scale are considered to be destructive. With each point increase on the Richter Scale, the damage becomes ten times worse. Ernest has the following readings and populations of the four areas of the city, which are to be the hardest hit. M=log(i/s)+5 where i is the intensity, s is the standard earthquake and M is magnitude. In his model, the standard earthquake is 10 microns. He needs to find the magnitude of the earthquake at each location and recommend to the fire department which area they should prepare to visit first.

 

[Harry_the_cat]

Firstly, for each area A to D, you need to substitute the intensity (i) and s=10 into the formula given to calculate the magnitude of the earthquake in each area.

Have you done that?

 

[Deleted member 4993]

Ernie has been watching an earthquake building near Irvine, California. Earthquakes that measure more than 5 on the Richter Scale are considered to be destructive. With each point increase on the Richter Scale, the damage becomes ten times worse. Ernest has the following readings and populations of the four areas of the city, which are to be the hardest hit. M=log(i/s)+5 where i is the intensity, s is the standard earthquake and M is magnitude. In his model, the standard earthquake is 10 microns. He needs to find the magnitude of the earthquake at each location and recommend to the fire department which area they should prepare to visit first.

Did you follow the advice provided in response #2?

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[TheWiseBoy]

Firstly, for each area A to D, you need to substitute the intensity (i) and s=10 into the formula given to calculate the magnitude of the earthquake in each area.

Have you done that?

Yes, I got
A: 5.499 (Magnitude)
B: 5.7
C: 5.4
D: 6
But do I just say that Ernie should recommend the fire department to visit the area with highest magnitude (Area D) first?
I don't know how the population could affect the calculation to determine where the department should head first.

 

[Deleted member 4993]

I don't know how the population could affect the calculation to determine where the department should head first.

That is an excellent point - but as the problem stands we do not have any data given in the problem-statement above. If I were given this problem, I would have made decision from the calculation above - but add a comment about your concern.

 

[BigBeachBanana]

Yes, I got
A: 5.499 (Magnitude)
B: 5.7
C: 5.4
D: 6
But do I just say that Ernie should recommend the fire department to visit the area with highest magnitude (Area D) first?
I don't know how the population could affect the calculation to determine where the department should head first.

You can look at the Expected Magnitude using population as weights.

\(\displaystyle \text{Total Population} = 45600\)
\(\displaystyle E(Magnitude)=5.499 \times \frac{12000}{45600} + \dots + 6 \times \frac{9540}{45600} \approx 5.62 \)
Both the magnitude of B and D are both greater than the average 5.62, but D > B so you should recommend D.

 

[Dr.Peterson]

You can look at the Expected Magnitude using population as weights.

\(\displaystyle \text{Total Population} = 45600\)
\(\displaystyle E(Magnitude)=5.499 \times \frac{12000}{45600} + \dots + 6 \times \frac{9540}{45600} \approx 5.62 \)
Since the magnitude of B and D are both greater than the average 5.62, but D > B so you should recommend D.

I'm not sure why you'd do that.

It seems to me that the damage is not proportional to magnitude, but to intensity; so there might be reason to multiply the latter by population (if you can believe that damage, and its effect on people, doesn't differ between different types of buildings).

A real-life decision would probably be based on other factors.

But I think it would help a lot if we knew the context of the question. Is this from a class on logarithms, where they just want you to use logs and don't care about real-life issues; or from a class on public safety or something, where more has been taught than we see here?

 

[Harry_the_cat]

Interesting problem.

As intensity increases, the magnitude increases - you can see this from the formula.

So you could rank the "severity" of the earthquake from the intensities without even calculating magnitude.

Calculating magnitude, though, shows that all earthquakes are destructive (>5) and some action needs to be taken by the fire dept.

So many other factors come into play though, eg strength of the buildings (are high rise office buildings built so they are more or less susceptible to earthquake damage?), what demographic live in inner city residential (more older people who may require more assistance?).

Based just on magnitude (or intensity) then D should be visited first, as others have said.

Based on the number of possible injuries (and since all earthquakes are >5 ie destructive), there is also an argument to send the fire dept to C based on population.

I think whatever conclusion you come to you need to justify it clearly.

 

[TheWiseBoy]

I'm not sure why you'd do that.

It seems to me that the damage is not proportional to magnitude, but to intensity; so there might be reason to multiply the latter by population (if you can believe that damage, and its effect on people, doesn't differ between different types of buildings).

A real-life decision would probably be based on other factors.

But I think it would help a lot if we knew the context of the question. Is this from a class on logarithms, where they just want you to use logs and don't care about real-life issues; or from a class on public safety or something, where more has been taught than we see here?

Yes, this is just a practice problem from a math class. I agree that they only care about the mathematical process.