(a)
the amount of money after 0 years = 500
the amount of money after 1 year = 500 * 1.015
the amount of money after 2 years = 500 * 1.015 * 1.015
the amount of money after t years = 500 * 1.015t
f(t) = 500 * 1.015t
(b)
We want to find the value of t when f(t) = 800
800 = 500 * 1.015t
1.6 = 1.015t
log( 1.6 ) = log( 1.015t )
log( 1.6 ) = t log( 1.015 )
log( 1.6 ) / log( 1.015 ) = t
31.568 ≈ t
Since interest is added annualy, it would take 32 years for the account to have $800 .
( After 31 years, it has $793.26 . After 32 years, it has $805.16 .)