Question 553504: Meteorologists can approximate the duration of a storm by using the formula T=.07D^3/2, where T is the time in hours that a storm of diameter D (in miles) lasts.
The National Weather Service reports that a storm 4 miles in diameter is headed toward New Haven. How long can the residents espect the storm to last?
Found 2 solutions by rapaljer, nyc_function:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The trick here is to know what D^3/2 means. For a fractional exponent like this, you take the ROOT of the denominator of the fraction, and RAISE to the POWER of the numerator. This means to take the 2nd root (i.e., square root) of D and raise to the power of 3 (i.e., cube it).
T=.07D^3/2
T=.07*4^(3/2)
 hours, or about a half hour.
For additional explanation on FRACTIONAL EXPONENTS, you should see my "Intermediate Algebra: One Step at a Time". The easiest way to find this website is by use of the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of this page is a link that will take you to my FREE Homepage. Look near the top of this page for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Intermediate Algebra" and look in Chapter 3 for the section "3.05 Fractional Exponents." The lesson is complete with explanations, examples, and exercises with all the answers. You will especially like the "MATH IN LIVING COLOR" explanations that go with this section. I think you will find that my explanations are a LOT easier to understand than the traditional textbooks you are probably using.
Happy New Year!! My Email address is rapaljer@seminolestate.edu if you need to contact me!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by nyc_function(2741)  (Show Source):
You can put this solution on YOUR website! Let D = 4 in the equation and solve for T.
T = 0.07D^(3/2)
T = 0.07(4)^(3/2)
T = 0.07(sqrt4{4})^3
T = 0.07 times (2)^3
T = 0.07 times 8
T = 0.56
We now convert 0.56 to time in hours.
0.56 times 60 minutes in one hour = 33.6 minutes.
Now, multiply 0.6 (which is the decimal part of 33.6) times 60 = 36 seconds.
Final answer for T = 0.0 hours, 33 minutes and 36 seconds.
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