1. Function

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

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: $d = 20 + 60(0.95)^t$??

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

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

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: $d = 20 + 60(0.95)^t$??

Could someone help me with both a and b pls?
[FONT=Arial]Thanks.
For a, yes but I would write $C(t) = 20 + 60(0.95)^t=d$

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

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