Question 1040411: Help!
1.
The fox population in a certain region has a relative growth rate of 7% per year. It is estimated that the population in 2013 was 18,000.
n(t) = 18,000e^{0.07t}
After how many years will the fox population reach 22,000? (Round your answer to one decimal place.)
2. At 8:30 a.m., a coroner was called to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person's temperature twice. At 9:00 a.m. the temperature was 93.4°F, and at 11:00 a.m. the temperature was 89.2°F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula
t=-10ln T-70/98.6-70
where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person's body. (This formula is derived from a general cooling principle called Newton's Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6°F at death, and that the room temperature was a constant 70°F.) Use the formula to estimate the time of death of the person. (Round your answer to the nearest hour.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 1. n(t)=18000e^0.07t
22,000=18000e^0.07t
divide both sides by 18000
22/18=e^0.07t=11/9
Take ln of both sides, because ln reverses e. ln *e^0.07t=0.07t. The e disappears
ln(11/9)=0.07t. Divide everything by 0.07 and then round at the end.
t=2.9 years
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check with 3 years, which should be more: 18000*e^(0.21)=22206
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2. t=-10 ln(t-70)/(98.6-70)
t=-10 ln(93.4-70)/28.6=-10(ln(23.4)/28.6=-10*(-0.200)=2 hours
t=-10ln(89.2-70)/28.6)=-10ln(19.2/28.6)=3.98 hours.
Time of death was 7 a.m. This is consistent with the 9 a.m. and 11 a.m. temperatures.
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