Integrate both sides

At t = 0 ,T = 370K

Hence h =ln|70|

ln|370-340| - ln|70| = 25k

ln|30/70| = 25k

k = (ln|3/7| )/25

c =25 ln|70| / ln|3/7|

Put this in the equation and T = 310 to get the value of t

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Another thing the sign of k has come out to be negative thus we can see that the temperature is decreasing, (something you can observe by reading the question)