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# C4 Differentiation Questions - Rates of Change Homework Help :) watch

1. 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.
2. (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 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...
3. Ahh thanks, just had a bit of a blank moment, yep I can do the rest thanks for the help

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