#### Answer

$a)A_{15}=0.01\times 2^{15-1}=163.84\$ $
$b) S_{15}=0.01\times \left( 2^{15}-1\right) 327.67\$ $

#### 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) $
$a)A_{15}=0.01\times 2^{15-1}=163.84;$
$b) S_{15}=0.01\times \left( 2^{15}-1\right) 327.67\$ $