<p>Ok, this is under the unit analysis section:</p>
<p>We can express the radius of the fireball (resulting from a bomb) R in terms of t, ρ and E as R=const2x E^(1/x)t^(-y/x)ρ^(−z/x).
Verify the relationship between R and t (That is R is proportional to t^(–y/x)) by plotting log (R) vs log (t) using the information provided in the pictures.
Fit the data of log (R) vs log (t) with a straight line. What is the slope of the
fit? What does the slope mean? Can you see why we are plotting log (R) vs
log (t) instead of R vs t?</p>
<p>Ps. I have found z= 1 y= -2 and x= 5 for the values in the R=… equation.</p>
<p>Basically, the pictures show the fireballs of a bomb with the diameter(m) at certain times(ms):
6ms–80m
120ms–110m</p>
<ul>
<li>Is it me, or is the question too vague? I am trying to understand what it’s asking and how I should answer.</li>
</ul>
<p>Thank you in advance.</p>
<p>Your expression is hard to follow (like what does const mean, a constant?), but here’s my best guess.
You plot this thing normally, and you get an exponential curve.
Plot log(R) and log(t), and ignoring the other stuff, you get log(R) = (-y/x)log(t), from the logarithm rules, which as you can see, will graph as a straight line with slope of (-y/x). I guess they want you to see that graphing log(R) and log(t) will yield a linear line of best fit (By the way, this kind of transformation is something discused in AP Statistics)</p>
<p>Gator, year it is supposed to be a constant. It is exactly how it is written on the problem. What do you mean by “plot this thing” normally? Can you guess what they want you to do with the information on the picture and take a shot at the other questions?</p>
<p>Anyway, you have been really helpful already, thanks for the help once again.</p>
<p>What I meant by plot it normally was if you graph the function as you wrote it.</p>
<p>In statistics, doing this, as in transforming a function into an equation of a line is called regression. We do this regression process because it’s easier to say something about a straight line than other functions.</p>
<p>For the problem, one thing you could say is everytime log(t) is increased by 1, log(R) will increase by (-y/x) [That’s what the slope means]</p>
<p>I have no idea what x, y, or z represent in the problem, so I would just plug in the values that you got for y and x into the slope</p>