Answer:
Step-by-step explanation:
Use Newton's Law of Cooling here:
[tex]T(t)=T_s+(T_0-T_s)^{-kt[/tex]
where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:
[tex]53=35+(73-35)^{-35k[/tex] which can simplify a bit to
[tex]53=35+(38)^{-35k[/tex] and [tex]18=38^{-35k[/tex]
Take the natural log of both sides:
[tex]ln(18)=ln(38)^{-35k[/tex]
Taking the natural log allows us to pull that exponent down out front:
[tex]ln(18)=-35k*ln(38)[/tex]
and now we can divide both sides by ln(38) to get
-35k = .794585 so
k = -.023
Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:
[tex]T(t)=35+(38)^{70(-.023)[/tex] and
[tex]T(t)=35+(38)^{-1.61[/tex] and
[tex]T(t)=35+.0028612013[/tex] and
T(t) = 35 F, basically the temp of the fridge, which is not surprising!
