# Function

#### foreverbrokenpromises

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

MHF Hall of Honor
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, $$\displaystyle C(t) = 20 + 60(0.95)^t\rightarrow C'(t)=60ln\left(\frac{19}{20}\right)\left(\frac{19}{20}\right)^t$$

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

Last edited: