Question

A breeding group of beavers is introduced into a protected area. After t years the number of beavers in the area is modeled by the function

N(t)= 54/0.35+0.68^t

1. How many beavers were initially introduced?
2. Estimate the number of beavers after 5 years.
3. Determine the change in the beaver population between t = 5 and t = 10.

(Note: All answers are whole numbers.)

Answer 1

The answers that I have so far are (I am not sure if I did them right):

1. N(t)= 54/0.35+0.68^0 = 40
2. N(t)= 54/0.35+0.68^5 = 109
3. I am not sure?

Answer 2

For initial result put t=0

Answer 3

question #1
you have to evaluate N(0)

Answer 4

yup and for #2 put t=5

Answer 5

1. 40
2. 109
3. ?

Answer 6

as change is n(5) - n(10)
put t= 5 and t=10 and subtract

Answer 7

yes! for third part we have to compute this:
\[{N\left( 5 \right) - N\left( 0 \right) = ...?}\]

Answer 8

I am not sure exactly how to compute that what do I plug in?

Answer 9

is your formula like this:
\[N\left( t \right) = \frac{{54}}{{0.35 + 0.68t}}\]

Answer 10

from 10 to 5
n(10) = 54/(.35+(.68^(10)))

Answer 11

@Michele_Laino that's how my formula is.

Answer 12

sorry ! Is it like below:
\[\Large N\left( t \right) = \frac{{54}}{{0.35 + {{0.68}^t}}}\]

Answer 13

yes

Answer 14

yup ^ this power operator.

Answer 15

then if t=0, we have:
\[\Large N\left( 0 \right) = \frac{{54}}{{0.35 + 1}} = ...?\]

Answer 16

40

Answer 17

correct!

Answer 18

if t=5, then we have:
\[\Large N\left( 5 \right) = \frac{{54}}{{0.35 + {{0.68}^5}}} \cong 109\]

Answer 19

so do I just go 109-40=69?

Answer 20

nope i dont think so

Answer 21

for t=10, we have:
\[\Large N\left( {10} \right) = \frac{{54}}{{0.35 + {{0.68}^{10}}}} \cong 145.5\]

Answer 22

3. Determine the change in the beaver population between t = 5 and t = 10.


here t is 10 and 5
implies 145-109 =?

Answer 23

so you have to do this:
\[\Large N\left( {10} \right) - N\left( 5 \right) = 145.5 - 109 = ...?\]

Answer 24

145.5-109=36.5

Answer 25

that's right!

Answer 26

yup in whole no.

Answer 27

yes! @AdityaOS is right!

Answer 28

So the answers are:

1. 40
2. 109
3. 36.5

but isn't 36.5 not in whole number

Answer 29

you can round off 36.5 to 37

Answer 30

oh ok thank you @Michele_Laino and @AdityaOS

Answer 31

:)