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The question:

The temperature of a steak that's being put into the oven can be describe with

*T(x) = 175-153e*

^{-kx}where T(x) is the temperature in degrees Celsius

*t*minutes after the steak has been put into the oven. After 30 minutes the steak's temperature is 50 degrees Celsius. At which rate is the temperature changing then?

This is my solution:

T(30)=50

50=175-153e

^{-50k}

-125=-153e

^{-50k}

125/153 = e

^{-50k}

ln (125/153) = -50k

k = ln(125/153)/-50, approximately 0.004

T(x)=175-153e

^{-0.004x}

T'(x)=0.612e

^{-0.004x }T'(30)=0.612e

^{-0.004(30)}, approximately 0.54

Answer: the steak's temperature is changing by 0.54 degrees Celsius/min, after 30 minutes

Would really appreciate feedback on this!