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Ksju [112]
3 years ago
12

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

temperature of 190◦C. Being a mathematician, she knows that the temperature T of the pie after t minutes of baking will be given by T(t) = 190 − Ae−kt , where A and k are constants. After 14 minutes of baking she notices that the temperature of the pie is 114◦C, while after 28 minutes it is 152◦C. Determine the constants A and k
Mathematics
1 answer:
pychu [463]3 years ago
7 0

Answer:

A=152

K= -Ln(0.5)/14

Step-by-step explanation:

You can obtain two equations with the given information:

T(14 minutes) = 114◦C

T(28 minutes)=152◦C

Therefore, you have to replace t=14, T=114 and t=28, T=152 in the given equation:

114=190-Ae^{-14k} (I) \\152=190-Ae^{-28k}(II)

Applying the following property of exponentials numbers in (II):

e^{a}.e^{b}=e^{a+b}

Therefore e^{-28k} can be written as e^{-14k}.e^{-14k}

152=190-Ae^{-14k}.e^{14k}

Replacing (I) in the previous equation:

152=190-76e^{-14k}

Solving for k:

Subtracting 190 both sides, dividing by -76:

0.5=e^{-14k}

Applying the base e logarithm both sides:

Ln(0.5)= -14k

Dividing by -14:

k= -Ln(0.5)/14

Replacing k in (I) and solving for A:

Ae^{-14(-Ln(0.5)/14)}=76\\Ae^{Ln(0.5)} =76\\A(0.5)=76

Dividing by 0.5

A=152

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