Laura
Ralston>Math 1111 Project Three
Laura
Ralston>Math 1111 Project Three
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Math 1111 Project Three 50 points ---5 points each Compound Interest: On the occasion of the birth of their first grandchild, two proud grandparents deposit $5000 in a certificate of deposit (CD) in the child's name. The CD pays an annual interest rate of 8% and it matures in 18 years, just in time for the child to begin college. 1. Determine the amount that will have accumulated after 18 years if the interest is compounded quarterly?
2. What if the interest is compounded continuously?
Mortgage: There is a relationship between the mortgage amount, the number of payments, the amount of the payment, how often the payment is made, and the interest rate. The following formula illustrate the relationship:
where P = the payment, r = the annual rate, M = the mortgage amount, t = the number of years, and n = the number of payments per year. 3. Find the monthly payments on a $100,000, 30-year mortgage, with monthly payments at 9.5%.
Drug Concentration: Sometimes after a patient takes a drug, the amount of medication A in the bloodstream can be modeled by A=Ce-rt where C is the initial concentration in milligrams per liter, r is the hourly percentage decrease (in decimal form) of the drug in the bloodstream and t is the elapsed time in hours. 4. Suppose you administer a drug whose concentration is initially 2 milligrams per liter and that the hourly percentage decrease is 20%. Find the drug concentration after 3.5 hours. Demand: The demand equation for a product is given by  where p is the price and x is the number of units. 5. Find the price, p, for a demand of x = 500 units.
Earthquakes: The Richter scale is used to measure the intensity of earthquakes. Intensity corresponds to the amount of energy released by an earthquake. If R is the intensity of an earthquake, A is the amplitude (measured in micrometers) and P is the period (the time of one oscillation of the earth's surface, measured in seconds), then
6. Find the intensity of an aftershock with a period of 0.07 and an amplitude of 2500 micrometers.
Sound: Use the mathematical model for power gain,
7. Determine the power gain, G, in decibels, for an amplifer with an output P0 of 20 watts and an input Pi of 1.5 watts. Round to five decimal places, if necessary. Barometric Pressure: The function defined by f(x) = 27 + 1.105 log(x+1) approximates the barometric pressure in inches of mercury at a distance x miles from the eye of a typical hurricane. 8. Approximate the pressure 9 miles from the eye of the hurricane. Round answer to two decimal places, if necessary.
Salinity: The salinity of the oceans changes with latitude and with depth. In the tropics, the salinity increases on the surface of the ocean due to rapid evaporation. In the higher latitudes, there is less evaporation and rainfall causes the salinity to be less on the surface than at lower depths. The function given by f(x) = 31.5 + 1.1 log(x+1) models salinity to the depths of 1000 meters at a latitude of 57.5°N. The variable x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. 9. Estimate the salinity at a depth of 500 meters.
Forensics: The formula for Newton's Law of Cooling, which can be expressed using the formula:
Inspector Ralston is called to the scene of a murder. The victim is lying in a room that has a constant temperature, C, of 75°F. The victim's body temperature is currently T= 81.2°F, down from the normal body temperature of 98.6°F (T0). After considering the height and weight of the victim, Ralston arrives at a value of k =10 for time measured in hours. 10. How long has the victim been dead? Round answer to one decimal place.
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