Need help in finding an equation to fit these points

jared_dx_58

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hi! i have a problem regarding maximum exposure time to different sound levels.

lets say you are allowed to be exposed to a sound level of 90 decibels for a maximum of 8 hours
for every 5 decibels above 90 decibels, the maximum allowable exposure time is halved. so if the sound level is 95 decibels, you can only be exposed to it for 4 hours. if sound level is 100 decibels, only 2 hours. On the contrast, for every 5 decibels below 90 decibels, maximum exposure time is doubled. so, you can be exposed to 85 decibels for 16 hours, 80 decibels for 32 hours, and so on. what is the function or equation that will relate the sound level to maximum exposure time? really need help with this please
 
hi! i have a problem regarding maximum exposure time to different sound levels.

lets say you are allowed to be exposed to a sound level of 90 decibels for a maximum of 8 hours
for every 5 decibels above 90 decibels, the maximum allowable exposure time is halved. so if the sound level is 95 decibels, you can only be exposed to it for 4 hours. if sound level is 100 decibels, only 2 hours. On the contrast, for every 5 decibels below 90 decibels, maximum exposure time is doubled. so, you can be exposed to 85 decibels for 16 hours, 80 decibels for 32 hours, and so on. what is the function or equation that will relate the sound level to maximum exposure time? really need help with this please
What are your thoughts?

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Lets say you are allowed to be exposed to a sound level of 90 decibels for a maximum of 8 hours. For every 5 decibels above 90 decibels, the maximum allowable exposure time is halved. So if the sound level is 95 decibels, you can only be exposed to it for 4 hours. If sound level is 100 decibels, only 2 hours. On the contrast, for every 5 decibels below 90 decibels, maximum exposure time is doubled. So, you can be exposed to 85 decibels for 16 hours, 80 decibels for 32 hours, and so on. What is the function or equation that will relate the sound level to maximum exposure time?

really need help with this please
When you plotted the given data points, what sort of curve did you see? What sort of equation did this suggest? What sort of equations have you recently studied?

Please be complete. Thank you! ;)
 
i do know that it's a curve with the x and y axis as the asymptotes, in quadrant 1. that's really all i could get so far. I've tried numerous equations like x=1/y and such, but can't really capture the equation....
 
i do know that it's a curve with the x and y axis as the asymptotes, in quadrant 1. that's really all i could get so far. I've tried numerous equations like x=1/y and such, but can't really capture the equation....

Which class has assigned this problem?

Did you make a table Like

90 .............. 8
95 .............. 4
100............. 2
105............. 1
110............. 1/2
115............. 1/4

Are you allowed to use software like MS-Excel?

Have you taken a course in calculus and Differential equations?
 
i do know that it's a curve with the x and y axis as the asymptotes, in quadrant 1. that's really all i could get so far. I've tried numerous equations like x=1/y and such, but can't really capture the equation....
What kind of equation did they give you for decibels (and earthquakes, and light intensity, etc)? Does this look familiar? ;)
 
we are allowed to use excel. this is actually an ergonomics questions, so no formulas given, but we had to find one.
 
we are allowed to use excel. this is actually an ergonomics questions, so no formulas given, but we had to find one.

So make a chart - like I proposed.

Use excel to plot it and find the best-fit trend-line equaton.
 
I have another way you can reason this out without using Excel. Think about the data points you know. If you plot the data on a graph, the decibels will be the x-coordinates, and the maximum exposure time will be the y-coordinates. Look at the maximum exposure times: 1 hour, 2 hours, 4 hours, etc. What pattern do you notice in those values? So based on that, you can extrapolate that your equation must be y=2^(some expression in x). But notice that the exposure times are decreasing as the decibels go up. What does that suggest you should do to your equation? Next look at the intervals. For every 5 decibels the sound goes up, the exposure time gets halved. Can you adjust your equation to account for this? And finally, look at where the maximum exposure time is 1. Since 2^0 = 1, you know that (expression in x) must be 0 at that point. What does that tell you about your equation?
 
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