Chapter 2 - Functions - 2.5 Preview of Composite and Inverse Functions - Exercises and Problems for Section 2.5 - Exercises and Problems - Page 103: 51

$f(g(n))=20+\frac{50}{9} 2^{-n}$ gives the temperature, $H$, in degrees Celsius after $n$ hours.

We have $$ H=f(g(n))=f\left(68+10 \cdot 2^{-n}\right)=\frac{5}{9}\left(68+10 \cdot 2^{-n}-32\right)=20+\frac{50}{9} 2^{-n}, $$ and $f(g(n))$ gives the temperature, $H$, in degrees Celsius after $n$ hours.