#### Answer

$a)A_{12}=0.01\times 2^{12-1}=0.01\times 2^{11}=20.48\$ ;$
$b)S_{12}=0.01\times \left( 2^{12}-1\right) =40.95\$ $

#### Work Step by Step

Amount earned on the indicated day can be calculated with using simple geometric sequence formula
$A_{n}=0.01\times 2^{n-1}$
And the total amount earned will be
$
S_{n}=\dfrac {A_{1}\left( 1-r^{n}\right) }{1-r}=\dfrac {0.01\times \left( 1-2^{n}\right) }{1-2}=0.01\left( 2^{n}-1\right) $
$a)A_{12}=0.01\times 2^{12-1}=0.01\times 2^{11}=20.48\$ ;$
$b)S_{12}=0.01\times \left( 2^{12}-1\right) =40.95\$ $