Hey there! Sign in to join this conversationNew here? Join for free
Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi, if anybody could help me on these questions that would be great! I've tried to answer them but I'm not sure if what I've done is correct.

    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=1000-Ae-0.4t where A is a constant. Given that there are 663 deer in the park after 2 years,

    a) Calculate, to 3 significant figures, the value of A.
    b) Calculate, to 3 significant figures, the number of deer introduced into the park.
    c) Calculate, to 3 significant figures, the number of deer 10 years after they have been introduced into the park.
    d) Find the rate at which the deer population is increasing after 5 years.

    Here's what I've done so far:

    a) 663=1000-Ae^-0.4(2)
    337=Ae^-0.8
    A=750

    b) P=1000-750e^-0.4(0)
    P=1000-750
    P=250

    c) P=1000-750e^-0.4(10)
    P=1000-750e^-4
    P=986 (3sf)

    d) I assume it involves dP/dt = ??
    But I don't even know where to start.

    Thanks for the help in advance.
    Offline

    13
    ReputationRep:
    (Original post by student832)
    Hi, if anybody could help me on these questions that would be great! I've tried to answer them but I'm not sure if what I've done is correct.

    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=1000-Ae-0.4t where A is a constant. Given that there are 663 deer in the park after 2 years,

    a) Calculate, to 3 significant figures, the value of A.
    b) Calculate, to 3 significant figures, the number of deer introduced into the park.
    c) Calculate, to 3 significant figures, the number of deer 10 years after they have been introduced into the park.
    d) Find the rate at which the deer population is increasing after 5 years.

    Here's what I've done so far:

    a) 663=1000-Ae^-0.4(2)
    337=Ae^-0.8
    A=750

    b) P=1000-750e^-0.4(0)
    P=1000-750
    P=250

    c) P=1000-750e^-0.4(10)
    P=1000-750e^-4
    P=986 (3sf)

    d) I assume it involves dP/dt = ??
    But I don't even know where to start.

    Thanks for the help in advance.
    Well yes you find  \frac{dP}{dt} and the simply substitute in t = 5.
    To differentiate P simply differentiate the first term (1000), the differentiate the exponential term and add the two results together. Considering this is C4 you should know how to differentiate exponentials...
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ahh thanks, just had a bit of a blank moment, yep I can do the rest thanks for the help
 
 
 
Poll
“Yanny” or “Laurel”
Help with your A-levels

All the essentials

The adventure begins mug

Student life: what to expect

What it's really like going to uni

Rosette

Essay expert

Learn to write like a pro with our ultimate essay guide.

Uni match

Uni match

Our tool will help you find the perfect course for you

Study planner

Create a study plan

Get your head around what you need to do and when with the study planner tool.

Study planner

Resources by subject

Everything from mind maps to class notes.

Hands typing

Degrees without fees

Discover more about degree-level apprenticeships.

A student doing homework

Study tips from A* students

Students who got top grades in their A-levels share their secrets

Study help links and info

Can you help? Study help unanswered threadsRules and posting guidelines

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.