For 10 13 use the following situation A potato is put into a

For 10 13, use the following situation: A potato is put into an oven that has been heated to 350°F. Its temperature as a function of time is given by T (t) a(1-e+b. The potato was 50BF when it was first put into the oven. 11. What is the value of a in this context? Explain. 12. If the potato is 60°F after 2 minutes, what is the value of k? Explain. 13. When will the potato reach 150°F? Explain.

Solution

10) given that at t = 0 , temperature = 50

T(0) = a(1-e⁰ ) + b = 50

a(1-1) +b = 50 hance b =50

11) similaly at t = infinity Temperature = 350

so a+b = 350 hance a = 300

12) T(2) = 300(1-e^k(2) )+50 = 60

k = -0.017

13) T = 150

150 = 50 + 300(1-e^(-0.017t)

1-e^(-0.017t) = 100/300

e^{(-0.017t) = 1-(1/3) = 2/3}

^{-0.017t = ln(2/3)}

^{t = 23.85 minutes}