Question

The electrical power for an implanted medical device decreases by 0.1% each day.

a. Find a formula for the nth term of the geometric sequence that gives the percent of the initial

power n days after the device is implanted.

Answer 1

$1-0.1\% = 1-0.001 =0.999$

After $n$ days the value of the device depreciates $n$ times with a factor 0.999. The value of the device after $n$ days is

$a_n=(initial value) (common ratio)^n$

$=1(0.999)^n = (0.999)^n$

The values of the device form a geometric sequence with $a_1=0.999$ and $r =0.999$

The formula for the $n$ th term of the geometric sequence that gives the percent of the initial power $n$ day after the device is implanted is $a_n=(0.999)^n$