TAOCP 7.2.2.2 Exercise 147

Exercise 147. [05] [05] Evaluate $C_{\max}$ in (66) for $d = 0, 1, 10, 20, 30$, using the default $C_0$ and $C_1$.

Verified: yes
Solve time: 57s

From (66), $C_{\max}(d) = C_0 C_1^d$. The default values given for the model parameters are $C_0 = 1$ and $C_1 = 2$, so $C_{\max}(d) = 2^d$.

For $d=0$,

$C_{\max} = 2^0 = 1$.

For $d=1$,

$C_{\max} = 2^1 = 2$.

For $d=10$,

$C_{\max} = 2^{10} = 1024$.

For $d=20$,

$C_{\max} = 2^{20} = 1{,}048{,}576$.

For $d=30$,

$C_{\max} = 2^{30} = 1{,}073{,}741{,}824$.