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

I think that the answers are (I just want to make sure):

1. 40
2. 109
3. 36.5 or 37 I think would be a whole number

Answer 2

@peachpi

Answer 3

N(t)= 54/0.35+0.68^0 = 40
N(t)= 54/0.35+0.68^5 = 109

Answer 4

I did the question and got partial points and would like to know where I went wrong?

Answer 5

You have written \(N(t) = \dfrac{54}{0.35} + 0.68^{t}\). This appears not to be what you intend. Please write clearly.

Answer 6

yes the first two are correct. For the third, it looks like you found N(10) instead of the calculating the rate of change

Answer 7

rate of change = [N(10) - N(5)] / (10 - 5)

Answer 8

@tkhunny sorry its N(t)= 54/(0.35+0.68^t)

Answer 9

So much better. Notation matters. Be careful.

Answer 10

misread that. The don't want the rate of change, just the change.
N(10) - N(5) is what you're asked for.

Answer 11

how do I use N(10) - N(5) do I plug something in?

Answer 12

yes, you plug in 5 and 10 for t.

This is what you had above.
N(t)= 54/(0.35+0.68^5) = 109
The N(t) should be N(5) because you substituted 5 for t. This is correct
N(5)= 54/0.35+0.68^5 = 109.

Answer 13

So plug in 10 for t to find N(10)

Answer 14

145.4979

Answer 15

do I subtract the two?

Answer 16

That's N(10). What else would you do to find a change or difference?

Answer 17

I am not sure? I thought it would be 145-109?

Answer 18

yes subtract

Answer 19

if I just do 145-109=36 before I got 36.5 and rounded it to 37 and I got partial points maybe its just 36

Answer 20

it seems so

Answer 21

ok thank you :)

Answer 22

you're welcome