Algebra help urgent

Question

Each week an album sells 6% fewer copies than it did the previous week. This week it sold 13,400 copies. At this rate, in how many weeks will it sell fewer than 2,000 copies? Round your answer up to the nearest week.

Answer 1

Hi,

This is an easy one!

Every week we are selling 6% less than the previous one. This is the same as selling 94% of the previous week.

Let´s say that n is the number of weeks.

Sales:

week 0: 13,400

Week 1: 13,400 x (1-6%) = 13,400 x 0.94

Week 2: 13,400 x 0.94 x 0.94 = 13,400 x 0.94^2

.....

Week n: 13.400 x 0.94^n

What is n so that 13,400 x 0.94^n = 2,000?

n= 30.67 or approximately 31 weeks.

Let me know if it is clear.

Thanks

Francisco