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

Isa Trevino 2021-05-07 Answered
Find a recursive rule that models the exponential decay of y=1600(0.97)t
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Expert Answer

Tuthornt
Answered 2021-05-08 Author has 107 answers

Use the explicit and recursive formulas for exponential decay to convert y into a recursive formula.
Explicit: Pn=P0(1+r)n
Recursive: Pn=(1+r)Pn1
Notice that 0.97 corresponds with 1+r. Therefore, r must equal 0.03. Fill in the recursive formula and simplify.
y(t)=1600(0.97)t
y(t)=(1+(0.03))y(t1)=(0.97)y(t1)

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