The amount of money left on a loan that Kira owes her grandmothers is represented by the function k (t) = 280 (.88) ^t where k (t) represents the amount of money left on a the loan and t represents the time, in years. Find r, the percent change and explain what it represents.

Question

Mathematics

Emiliano

Today, 06:12

The amount of money left on a loan that Kira owes her grandmothers is represented by the function k (t) = 280 (.88) ^t where k (t) represents the amount of money left on a the loan and t represents the time, in years. Find r, the percent change and explain what it represents.

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Tia Gray · Answer 1

Given:

k (t) = 280 (0.88) ^t

t = 1; t = 2; t = 3

k (1) = 280 (0.88) ¹ = 280 (0.88) = 246.40

k (2) = 280 (0.88) ² = 280 (0.7744) = 216.83

k (3) = 280 (0.88) ³ = 280 (0.681472) = 190.81

280 - 246.40 = 33.60 ⇒ 33.60/280 = 0.12

246.40 - 216.83 = 29.57 ⇒ 29.57/246.40 = 0.12

216.83 - 190.81 = 26.20 ⇒ 26.20/216.83 = 0.12

The rate is 0.12 or 12%