Elenathehomeschooler
  • Elenathehomeschooler
A hot bowl of soup cools according to Newton’s law of cooling. Its temperature (in degrees Fahrenheit) at time t is given by T(t)=68+144e^-.04t, where t is given in minutes. 3. What was the initial temperature of the soup? 4. What is the temperature of the soup after 15 minutes?
Mathematics
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SOLVED
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katieb
  • katieb
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Elenathehomeschooler
  • Elenathehomeschooler
@jim_thompson5910 help?
jim_thompson5910
  • jim_thompson5910
plug in t = 0. What do you get for T?
Elenathehomeschooler
  • Elenathehomeschooler
212 degrees

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More answers

jim_thompson5910
  • jim_thompson5910
correct. This is the initial temperature because it's the temperature when the time is t = 0 minutes
jim_thompson5910
  • jim_thompson5910
`What is the temperature of the soup after 15 minutes?` now plug in t = 15
Elenathehomeschooler
  • Elenathehomeschooler
im stuck can you help? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
show me what you have so far
Elenathehomeschooler
  • Elenathehomeschooler
\[T(15)=68+144e ^{-.04(15)}\]
jim_thompson5910
  • jim_thompson5910
good, now you just need to use a calculator to evaluate `68 + 144*e^(-0.04*15)`
Elenathehomeschooler
  • Elenathehomeschooler
\[T(15)=68+144e ^{-0.6}\]
jim_thompson5910
  • jim_thompson5910
btw the 'e' is a constant like 'pi' is (just a different fixed number)
Elenathehomeschooler
  • Elenathehomeschooler
okay
Elenathehomeschooler
  • Elenathehomeschooler
what do i do now?
jim_thompson5910
  • jim_thompson5910
what is the value of `68 + 144*e^(-0.04*15)` use a calculator. If you don't have one, use this http://web2.0calc.com/
Elenathehomeschooler
  • Elenathehomeschooler
147
jim_thompson5910
  • jim_thompson5910
did you get a whole number? or decimal number?
Elenathehomeschooler
  • Elenathehomeschooler
this is what the calculator said 147.028875597539816
jim_thompson5910
  • jim_thompson5910
I'm getting `147.0288756` so it looks like we both got the same
jim_thompson5910
  • jim_thompson5910
if you round to the nearest whole degree, then yes, it's 147 degrees F
Elenathehomeschooler
  • Elenathehomeschooler
so it will be 147 degrees F when it has been 15 min?
jim_thompson5910
  • jim_thompson5910
yes
Elenathehomeschooler
  • Elenathehomeschooler
yay! thanks
jim_thompson5910
  • jim_thompson5910
assuming they want you to round to the nearest whole number
jim_thompson5910
  • jim_thompson5910
no problem

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