Question

A pizza is removed from the oven at a temperature of 425 F. After 15 minutes, the pizza has

cooled to 200°F. Use a continuous exponential decay model to find the approximate decay

rate.


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Answer 1

Answer:

The decay rate is of 0.05 = 5% per minute.

Step-by-step explanation:

Continuous exponential decay model:

The exponential equation of decay for an amount, after t units of time, is given by:

$A(t) = A(0)e^{-rt}$

In which A(0) is the initial amount, e(approx 2.72) is the Euler value and r is the decay rate, as a decimal.

A pizza is removed from the oven at a temperature of 425 F.

This means that $A(0) = 425$

After 15 minutes, the pizza has cooled to 200°F.

This means that $A(15) = 200$, that is, when $t = 15, A(t) = 200$

We use this to find r.

$A(t) = A(0)e^{-rt}$

$200 = 425e^{-15r}$

$e^{-15r} = \frac{200}{425}$

$\ln{e^{-15r}} = \ln{\frac{200}{425}}$

$-15r = \ln{\frac{200}{425}}$

$r = -\frac{\ln{\frac{200}{425}}}{15}$

$r = 0.05$

The decay rate is of 0.05 = 5% per minute.