Question

The number of houses in a town has been growing according to the recursive rule Pn =Pn-1+30, with initial population P0 = 200

A. calculate P1 and P2
B. Find an explicit formula for Pn
C. Use your formula to predict the number of houses in 10 years.
D. When will the number of houses reach 400 houses?

Answer 1

what is the first term?

Answer 2

.. or rather to keep things numeralated: what is the zeroth term?

Answer 3

\[P _{0} = 200\] so P would = 200 ? I am not sure where to start with this question

Answer 4

Po is just a name for the very first term; think of it as a starting line.

Now we are told that each new term is 30 more than the previous term.

P1 is therefore Po+30
P2 is Po + 30 + 30
P3 would be Po + 30+30+30 and we start to see a pattern to be explicit about

Answer 5

Awww ok, so this would continue until i reach the goal?
Would I add P1 and P2 together to find B or am i approaching this the wrong why?

Answer 6

well, your confusing a few things. but you are on the right track.

Answer 7

the rule is: Pn = Pn-1 + 30 ... this says that for what ever term we want to know the value of, it is 30 more than the term before it. And we are also told the the whole thing starts out as Po = 200

P1 = Po + 30

P2 = P1 + 30 ; but P1 = Po + 30 giving us
= Po + 30 + 30

P3 = P2 + 30; but P2 = Po + 30 + 30
= Po + 30 + 30 + 30

etc

Answer 8

each term can now be expressed as the zeroth term and a multiple of 30; which helps us define the explicit rule

Answer 9

P1 = Po + 30(1)
P2 = Po + 30(2)
P3 = Po + 30(3)
...
Pn = Po + 30(n)

does that make sense?

Answer 10

I think so, I'm going to try it and see if I can get it and I'll let you know, Thank you.

Answer 11

good luck :)