Find a recursive rule that models the exponential decay of y=1600(0.97)^t

Find a recursive rule that models the exponential decay of $y=1600{\left(0.97\right)}^{t}$
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Tuthornt

Use the explicit and recursive formulas for exponential decay to convert y into a recursive formula.
Explicit: $Pn=P0{\left(1+r\right)}^{n}$
Recursive: $Pn=\left(1+r\right)Pn-1$
Notice that 0.97 corresponds with $1+r$. Therefore, r must equal $-0.03$. Fill in the recursive formula and simplify.
$y\left(t\right)=1600{\left(0.97\right)}^{t}$
$y\left(t\right)=\left(1+\left(-0.03\right)\right)y\left(t-1\right)=\left(0.97\right)y\left(t-1\right)$