Question

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.

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%