Math Is Fun Forum

natashabaker

Member

Registered: 2007-05-25

Posts: 10

differce equations questions

hey i need help with a few questions if anyone can assist

1. In the year 2000, there were 25000 visitors in a wildlife park using this difference equation
Vn+1= 1.2 Vn +4000
where Vn is the number of visitors in the Nth year, predict the number of visitors in 2002
A.25,000
B.29,000
C.34,000
D.44,800
E.57,760

2. A hockey club began a fundraising campaign to raise money for a new clubroom in the first year of fundraising they raised 15,000 after that the amount of money they raised each year increased by 5% each year by the end of the fifth year the total amount of money they raised was closest to-
A. $15,789
B. $18,750
C. $78,750
D. $82,884
E.  $95,721

3. A shrub, 20 cm high, was planted in a pot. After it was planted, its height increased by 8 cm in the first month by 4 cm in the second month and by 2cm in the third month assuming this pattern of growth continues, the shrub will grow to its maximum height of:
A. 35cm
B. 36cm
C. 37cm
D. 38cm
E.  40cm

they are the questions i'm stuck on at the moment thanks

U7109

Real Member

Registered: 2007-03-19

Posts: 485

Re: differce equations questions

Half of this stuff looks confusing, but I'll see if I can work it out. For the third question, I'm guessing that it's answer D or E. And I'm just guessing. But I can't help you with the second and first, and I'm very sorry about that, but I don't even know those.

Oh, and welcome to the forum, Natashabaker! You're making a good start on posting

---

"Reality leaves a lot to the imagination," ~ John Lennon

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: differce equations questions

thanks choco yeah they are confusing, good luck with them

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: differce equations questions

i've forgotten this one to
The difference equation
tn+1= a+n+5 where t1=3
Generates the sequence 3,11,27,59
The value of a is
A.1
B.2
C.3
D.8
E.11

Last edited by natashabaker (2007-05-28 20:52:51)

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: differce equations questions

The standard series way to answer all you questions.

aq,aq^2,aq^3,aq^4...aq^(n-1)

find the sum of them, you may find a formula of S.

However I can solve the first question in a tricky way:

Vn+1= 1.2 Vn +4000
Vn+1+20000= 1.2 Vn +24000
Vn+1+20000= 1.2 (Vn +20000)
So V[sub]2002[/sub]+20000=1.2²(25000+20000)
V[sub]2002[/sub]=44800

How did I come up with 20000 and 24000?
suppose
Vn+1+C=1.2Vn+1.2C
so
Vn+1=1.2Vn+0.2C
See what C is?

---

X'(y-Xβ)=0

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

Natashabaker , The answer for the first question given by you is the third option.. 44, 800...

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

I hope you got the answer now.. Do you want me to put down the steps?

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

Sorry the fourth option.. 44,800

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: differce equations questions

I hope you got the answer now.. Do you want me to put down the steps?

if you can please

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

From the question. Vn= the number of visitors in the nth year.. ..

Given that, in the year 2000, there were 25000 visitors..

V2000 = 25000...  so.. V(2000+1) = 1.2(V2000) + 4000.

V(2001) = 1.2(25000) + 4000.

V(2001) = 34, 000

That is the number of visitors in the year 2001 is 34,000

therefore for the year 20o2

V(2001+1) = 1.2 V(2001) + 4000

V(2002) = 1.2 ( 34,000) + 4000

V(2002) = 44,800

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

So, The number of visitors in the year 2002 is 44,800..

Have you got it?

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: differce equations questions

i understand that very clearly thanks alot sk

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

You are most welcome baker:)

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

Natashabaker,
A shrub, 20 cm high, was planted in a pot.
After it was planted, its height increased by 8 cm in the first month by 4 cm in the second month
and by 2cm in the third month assuming this pattern of growth continues,
the shrub will grow to its maximum height of:
A. 35cm
B. 36cm
C. 37cm
D. 38cm
E. 40cm

The answer for this question is the option C ---- 36 cm..

Last edited by sk (2007-05-30 21:03:32)

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

Initially, the shrub was 20 cm high.. the very first month.. its growing 8cm and the second month 4 cm and the third month 2 cm..

And this pattern is continuing. so the fourth month the height will increase 1 cm and the in the fifth month the height will increase 1/2cm and in the sixth month it will increase by 1/4 cm.. and so on..

so..  20 + 8+4+2+1+(1/2) + (1/4) + so on...

35 +  very small number.

Last edited by sk (2007-05-30 21:03:08)

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

Sorry dear 35 + 1/2 + 1/4 + very small numbers will come..

So the answer will be B. maximum of 36 cm.

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: differce equations questions

thanks SK that looks pretty straight forward

sk

Member

Registered: 2006-08-04

Posts: 19

Re: differce equations questions

You are most welcome  natasha..... :-)