Function

The temperature of a cup of coffee t minutes after it has been poured is described by the function \(\displaystyle C(t) = 20 + 60(0.95)^t \).

a. How many minutes does it take for the coffee to cool to a temperature of d degrees?


b. About how fast is the temperature dropping when t = 1?

For a. is it just: \(\displaystyle d = 20 + 60(0.95)^t \)??

Could someone help me with both a and b pls?
Thanks.

 

dwsmith

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Mar 2010
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The temperature of a cup of coffee t minutes after it has been poured is described by the function \(\displaystyle C(t) = 20 + 60(0.95)^t \).

a. How many minutes does it take for the coffee to cool to a temperature of d degrees?


b. About how fast is the temperature dropping when t = 1?

For a. is it just: \(\displaystyle d = 20 + 60(0.95)^t \)??

Could someone help me with both a and b pls?
Thanks.



For a, yes but I would write \(\displaystyle C(t) = 20 + 60(0.95)^t=d \)

For b, \(\displaystyle C(t) = 20 + 60(0.95)^t\rightarrow C'(t)=60ln\left(\frac{19}{20}\right)\left(\frac{19}{20}\right)^t\)

\(\displaystyle C'(1)=60ln\left(\frac{19}{20}\right)\left(\frac{19}{20}\right)^1=57\left(\frac{19}{20}\right)= 54.15\)
 
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