Quick questions on Exponential growth and decay (WACE Year 12 Mathematics Applications)

Q: What is off-by-one in the explicit rule?

t_n = t_1 r^n-1 uses the exponent n-1, because the first term has had no ratio applied yet. Mixing this with the value-after-n-years form V_0 r^n causes errors.

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What is off-by-one in the explicit rule?

Show answer

t_n = t_1 r^{n-1}

uses the exponent

n-1

, because the first term has had no ratio applied yet. Mixing this with the value-after-

n

-years form

V_0 r^{n}

causes errors.

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