Question

Funny, and somewhat tough question I found:

Suppose that in January 2013, there were 5000 radio stations in the US that played Justin Bieber's music, and that In July 2013, there were only 4000 radio stations in the US that played Justin Bieber's music.

Assuming that the rate of decline is proportional to the number of radio stations which play Justin Bieber's music, when would there only be 2000 radio stations which play Justin Bieber's music?

Answer 1

Options:

July 2014
January 2014
July 2015
January 2015

Answer 2

Let the rate of decline be d

Answer 3

Between January and July 2013 the rate was 0.8

Answer 4

And it's proportional to 5000

Answer 5

So d/5000=constant

Answer 6

I hope you can figure it out. My answer was not right. I got September 2015.

Answer 7

=0.00016

Answer 8

So d=0.00016*b

Answer 9

July 2013: d=0.00016*4000=0.64, b=4000*0.64=2560

Answer 10

January 2014: d=0.00016*2560=0.4096, b=2560*0.4096=1048.576

Answer 11

Wait...

Answer 12

The decline was 1000

Answer 13

My answer is C before any other answers are thrown out there.

Answer 14

The rate of decline is proportional... so the rate of decline isn't a constant

Answer 15

The rate of decline was 0.2, 0.2/5000=0.00004

Answer 16

So d=0.00004b

Answer 17

July 2013: d=0.00004*4000=0.16, b=4000*(1-0.16)=3360

Answer 18

January 2014: d=0.00004*3360=0.1344, b=3360*(1-0.1344)=2908.416

Answer 19

July 2014: d=0.00004*2908.416=0.11633664, b=2908.416*(1-0.11633664)=2570.06065

Answer 20

January 2015: d=0.00004*2570=0.1028, b=2570*(1-0.1028)=2305.804

Answer 21

July 2015: d=0.00004*2305.804=0.09223216, b=2305.804*(1-0.09223216)=2093.13472

Answer 22

Close enough; July 2015

Answer 23

What do you mean close enough.

Answer 24

i smell a diff eqn..

Answer 25

\[\Large b_{n+1}=(1-0.00004b_n)b_n\]

Answer 26

Write an explicit formula for that, b_0=5000

Answer 27

January 2015