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11-29-2012   #2
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by someday 1. A family of four is looking to purchase a home. The family has decided that they can mortgage a house for up to \$225,000. a.) In terms of paying less interest at the end of the loan: which would be more economical? A 30-year fixed rate at 8% or a 15-year fixed-rate at 7.5%? b.) Why would a family of four prefer to buy a house at a 30-year fixed rate mortgage loan versus a 15-year fixed rate mortgage loan? 2. Newton’s law of cooling is used in homicide investigations to help determine time of death. The normal body temperature of a human is 98.6degreesF. Immediately following death the body begins to cool. It is determined that the constant in newton’s law of cooling is approximately k=-0.1947 assuming time is measured in hours. Suppose that the body temperature of the surroundings if 60degreesF. a.) Find a function u(t) that models the temperature (t) hours after death. b.) If the temperature of the body is now 72degrees F, how long ago was the time of death? 3. The richter scale is one way of converting seismographic readings into numbers that provide easy reference for measuring the magnitude M of an earthquake. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures (x) millimeters has magnitude M(x) given by M(x)=log(x/x[0]) Where x[0]=10^-3 is the reading of a zero-level earthquake the same distance from its epicenter. Determine the magnitude of each of the earthquakes in the following problems: a.) Oregon coast march 15, 2008 at 7:44 am: seismographic readings of 878 millimeters 100 kilometers from the center. a. The greatest earthquake magnitude on U.S soil was in 1964 in Alaska. Seismographic readings of 1286325 millimeters 100 kilometers from the center.
1. a. For a mortgage of \$225,000
Total interest paid over 30 year at 8.0% is \$369,349.69
Total interest paid over 15 year at 7.5% is \$150,439.72
So the 15 year loan at 7.5% saves you much more in interest payments than the 30 year loan does.
b. It might be more economical to have the 30 year loan because the monthly payments are much lower than the 15 year loan, \$1650.97 versus \$2085.78.

2. The formula for Newton's Law of Cooling is:
T(t) = Ta + (T0 - Ta)e^(-kt)

72 = 60 + (98.6 - 60)e^(-0.1947t)
12 = 38.6e^(-0.1947t)
0.31088 = e^(-0.1947t)
ln(0.31088) = -0.1947t
-1.1683456/-0.1947 = t
t = 6 hrs
So the time of death was 6 hrs ago.

3. M(x)=log(x/x[0]) where x[0] = 0.001
M(x) = log(x/0.001) = log(1000*x)

a. M(878) = log(1000*878) = 5.94
b. M(1286325) = log(1000*1286325) = 9.11