at 0 months, Carson has 450, so say his total balance is "y", thus at 0 months
y = 450 ................................. 0 months
y = 70 + 450 .......................... 1 month
y = 70+70 + 450 ..................... 2 months
y = 70+70+70 + 450 ............... 3 months
y = 70+70+70+70+ 450 ........... 4 months
y = 70(4) + 450 ....................... 4 months
y = 70(x) + 450 ....................... x months
y = 70x + 450