The temperature, θ∘C\theta^\circ\text{C}θ∘C, of a liquid in a cooling tank, ttt minutes after cooling begins, is modeled by the equation
θ=B+150e−kt \theta = B + 150e^{-kt} θ=B+150e−ktwhere BBB and kkk are positive constants. Given that the initial temperature of the liquid is 175∘C175^\circ\text{C}175∘C,
find the value of BBB.
The temperature of the liquid 4 minutes after cooling begins is 67∘C67^\circ\text{C}67∘C.
Show that k=plnqk = p \ln qk=plnq where ppp and qqq are rational numbers to be found.
Hence find
the temperature of the liquid 8 minutes after cooling begins, giving your answer to 3 significant figures,
the rate of decrease of the temperature of the liquid 8 minutes after cooling begins. Give your answer in ∘C min−1^\circ\text{C min}^{-1}∘C min−1 to 3 significant figures.