C2 Help

11

Can anyone help me on part c of this question? a and b are straightforward, but c is a bit trickier.

3.A population of deer is introduced into a park. The population P at t years after the deer have been introduced is modelled by P=[2000a^t]/[4 + a^t]where a is a constant. Given that there are 800 deer in the park after 6 years,

(a)calculate, to 4 decimal places, the value of a,

(b)use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.

(c)With reference to this model, give a reason why the population of deer cannot exceed 2000.

4.Given that f(x)=[([2x^1.5] - [3x^-1.5])]^2 + 2

(a)find, to 3 significant figures, the value of x for which f(x) =5.
(b)Show that f(x) may be written in the form where A, B and C are constants to be found.

I think the answers have done the above question wrong. They hav added the powers, and multiplied the bases - school boy error!

Reply 1

insparato

15

(c)With reference to this model, give a reason why the population of deer cannot exceed 2000.

As P = 2000/1 + at^-1

4a^-1 tends to 0 as t tends to infinity.

So when p tends to 2000 but doesnt exceed it.

4)4.Given that f(x)=[([2x^1.5] - [3x^-1.5])]^2 + 2

(a)find, to 3 significant figures, the value of x for which f(x) =5.
(b)Show that f(x) may be written in the form where A, B and C are constants to be found.

This is wrong -- f(x)=[([2x^1.5] - [3x^-1.5])]^2 + 5 is the correct f(x) ive just done this question hehe.

so [([2x^1.5] - [3x^-1.5])]^2 + 5 = 5

[([2x^1.5] - [3x^-1.5])]^2 = 0

Square root both sides

[ 2x^3/2 - 3x^-3/2 ] = 0

So therefore 3x^-3/2 = 3x^-3/2

2/3x^-3/2 = x^-3/2

2/3 = x^-3/2 / ^-3/2

2/3 = x^-3

2/3 = 1/x

Reply 2

Srathmore

OP

11

Reply 3

Apagg

13

y^x * y^x = y^2x

(y^x)^x = y^xx

Reply 4

supernova2

11

Yeh I hate these delphis papers or whatever, there so much arder than just the past papers :frown:

Reply 5

*Katie*

1

I'm going crazy - can anyone help with part a?
I got to

2 2/3 = a^6

and I got stuck

Reply 6

samgurl

Srathmore

Can anyone help me on part c of this question? a and b are straightforward, but c is a bit trickier.

3.A population of deer is introduced into a park. The population P at t years after the deer have been introduced is modelled by P=[2000a^t]/[4 + a^t]where a is a constant. Given that there are 800 deer in the park after 6 years,

(a)calculate, to 4 decimal places, the value of a,

(b)use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.

(c)With reference to this model, give a reason why the population of deer cannot exceed 2000.

please could someone help me with part b and let me know if i got part a right

a) 800=2000a^6/4+a^6

3200+800a^6= 2000a^6
3200=1200a^6
2.6666=a^6
1.1776(4dp)=a

Reply 7

samgurl

bump

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