anonymous
  • anonymous
The temperature of a body is measured as 104oF. It is observed that the amount the temperature changes for each period of two hours is -0.3 time the difference between the previous period's temperature and the room temperature, which is 70oF. a. Write a recurrence relation for tn, the temperature of the body at the end of n 2-hour time periods.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
dT/dt = -0.3(T - 70)
anonymous
  • anonymous
\[t_{0} = 104\]
anonymous
  • anonymous
I had T(n) = -.03(104 - 70)

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anonymous
  • anonymous
so same thing
anonymous
  • anonymous
u know differential eqns?
anonymous
  • anonymous
oooo...somewhat...has been a while
anonymous
  • anonymous
dT/(T-70) = -0.3dt
anonymous
  • anonymous
\[\int\limits_{104}^{T}dT/(T-70) = -0.3\int\limits_{0}^{t}dt\]
anonymous
  • anonymous
need to keep it basice with recurrence relations
anonymous
  • anonymous
ln (t-70) = -0.3ln(34)t
anonymous
  • anonymous
thanks though!
amistre64
  • amistre64
so initial t{0} = 140 right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
t{n} = -0.3*[ t{n-1} - 70]
anonymous
  • anonymous
I havee that but can't get to work on calc
amistre64
  • amistre64
i havent used the calulator :) plug it in google to create a table if need be
anonymous
  • anonymous
gues i 'll do it by hand
anonymous
  • anonymous
how on google...tried wolfram once...pretty cool
anonymous
  • anonymous
Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours.
amistre64
  • amistre64
i just reiterete it over and over in the right place on google
amistre64
  • amistre64
-.3*( 104 - 70) -.3(-.3*( 104 - 70)-70) -.3(-.3(-.3*( 104 - 70)-70)-70) like that

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