Problem

Interpret the base in $M(t)=500\cdot~1.5^{t}$ as a recurrence factor and retained percentage, determine the yearly growth rate, verify the interpretation with $M(0)$ and $M(1)$, and distinguish the coefficient.

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base = 1.5; recurrence = M(t+1)=1.5M(t); retained = 150%; growth = 150%/year; check = M(1)=$750; coefficient distinction = 500 is initial balance

base = 1.5; recurrence = M(t+1)=M(t)+1.5; retained = 150%; growth = 50%/year; check = M(1)=$501.50; coefficient distinction = 500 is initial balance

base = 500; recurrence = M(t+1)=500M(t); retained = 500%; growth = 400%/year; check = M(1)=$750; coefficient distinction = 1.5 is initial dollars

base = 1.5; recurrence = M(t+1)=1.5M(t); retained = 150%; growth = 50%/year; check = M(0)=$500 and M(1)=$750; coefficient distinction = 500 is initial balance

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Interpret the base in \(M(t)=500\cdot~1.5^{t}\) as a recurrence factor and retained percentage, determine the yearly growth rate, verify the interpretation with \(M(0)\) and \(M(1)\), and distinguish the coefficient.

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