Respuesta :
Answer:
After 21.28  minutes will the coffee be only lukewarm (30∘C)
Step-by-step explanation:
Given -
A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day . The temperature of the coffee after t minutes is given by
         [tex]H = 87(2)^{\frac{-t}{14}}[/tex]
Let after [tex]t_{1}[/tex] time  H will be [tex]$30^\circ$[/tex]C
put t = [tex]t_{1}[/tex] Â , Â H = [tex]$30^\circ$[/tex]C
    [tex]30 = 87(2)^{\frac{-t_{1}}{14}}[/tex]
    [tex]\frac{30}{87} = (2)^{\frac{-t_{1}}{14}}[/tex]
   .3448275 = [tex](2)^{\frac{-t_{1}}{14}}[/tex]
   Taking logarithm both side Â
   [ [tex]log(2^{x}) = xlog2[/tex] ]
   log.3448275 = [tex]{\frac{-t_{1}}{14}}[/tex] log 2
   -.4581  =  [tex]{\frac{-t_{1}}{14}} \times.3010[/tex]
    [tex]{\frac{-t_{1}}{14}}[/tex]  =  -1.52
    [tex]t_{1}[/tex] = 21.28 minutes
