A video sharing website starts with 20,000 members. Each year it loses 25% of the members, but adds 10,000 new members after the reduction. Write a recursive rule to find the number of members for any year.

Question

anonymous · Answer

@LeeEtchison @bohotness

anonymous · Answer

@ambius @whydoihavetosignup1 @RAINIAR

anonymous · Answer

so, essentially there are two components to the change in population - probably a couple of ways to approach it... however, what we are looking for is an equation in the form of:

$$P_{n+1} = f(P_n)$$

meaning the next value of the population is equal to a function of the current value. I'll show you the first value:

$$P_{0} = 20000$$

what would $$P_1$$ equal?

anonymous · Answer

these are the choices they gave me

anonymous · Answer

Pleeeaasssee Hellpp

anonymous · Answer

Sorry... lots of stuff at once... okay so you notice I started the equation considering the "next" value in the equation - P(n+1). However, you can look at the equation interms of the "previous" value instead. This seems a little confusing, but it's not too bad once you get the hang of it.  So, instead of over-complicating it, I'll give you a hint.

The initial population is 20000, so:
$$P_1 = 20000$$

If I were to calculate the change in population after a year to determine P2 using the value of P1, how would I calculate it?

anonymous · Answer

Any ideas?

anonymous · Answer

Here's another hint; I can't give you much more than this without straight-up giving you the answer:

$$P_2 = 0.75P_1 + 10000$$