## KJ4UTS one year ago 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.)

1. KJ4UTS

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?

2. anonymous

For initial result put t=0

3. Michele_Laino

question #1 you have to evaluate N(0)

4. anonymous

yup and for #2 put t=5

5. KJ4UTS

1. 40 2. 109 3. ?

6. anonymous

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

7. Michele_Laino

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

8. KJ4UTS

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

9. Michele_Laino

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

10. anonymous

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

11. KJ4UTS

@Michele_Laino that's how my formula is.

12. Michele_Laino

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

13. KJ4UTS

yes

14. anonymous

yup ^ this power operator.

15. Michele_Laino

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

16. KJ4UTS

40

17. Michele_Laino

correct!

18. Michele_Laino

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

19. KJ4UTS

so do I just go 109-40=69?

20. anonymous

nope i dont think so

21. Michele_Laino

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

22. anonymous

3. Determine the change in the beaver population between t = 5 and t = 10. here t is 10 and 5 implies 145-109 =?

23. Michele_Laino

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

24. KJ4UTS

145.5-109=36.5

25. Michele_Laino

that's right!

26. anonymous

yup in whole no.

27. Michele_Laino

28. KJ4UTS

So the answers are: 1. 40 2. 109 3. 36.5 but isn't 36.5 not in whole number

29. Michele_Laino

you can round off 36.5 to 37

30. KJ4UTS

oh ok thank you @Michele_Laino and @AdityaOS

31. Michele_Laino

:)