## anonymous 3 years ago How do you solve this?? N = 3,500e^(k * 9.5)

1. anonymous

How do you solve this?? N = 3,500e^(k * 9.5)

2. anonymous

There's two variables...

3. anonymous

I know. Im supposed to solve for k. Does that help at least a little bit? @CalebBeavers

4. anonymous

Hmm, start off by dividing both sides by 3500

5. anonymous

So it would be N/3,500 = e^9.5k? @CalebBeavers

6. anonymous

Yeah, now take natural log of both sides

7. anonymous

So In(N/3,500) = 9.5k?

8. anonymous

Yep, now just divide by 9.5

9. anonymous

So In(N/3,500)/9.5 = k?

10. anonymous

Yep =D

11. anonymous

But the questions says to Use the function to find the value of the boat after 9.5 years. (Not this question, the question on my assignment.) Is that the boat value?

12. anonymous

so it gives you the function N = 3,500e^(kt) ?

13. anonymous

Well it didnt give me that but i asked the question earlier and someone said to use that equation.

14. anonymous

Hmmm. lets start over whats the original question and all the information it gives you?

15. anonymous

14. The exponential decay graph shows the expected depreciation for a new boat, selling for \$3500, over 10 years. Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years. @CalebBeavers

16. anonymous

Hmm so $\large f(t)=ae^{kt}$ use known information from the graph, say point (3,1500) the a is the value at the start so plug these in and solve for k $1500=3500e^{3k}$ when you know k you can plug it back in to solve for the value at 9.5 years

17. anonymous

So if i plugged in 9.5 it would look like 1500 = 3500e^(3 * 9.5)?

18. anonymous

No, we need to solve for k. t represents time, we know after 3 years it was 1500 so were plugging that in so we have one variable to solve for

19. anonymous

We need to solve for e?

20. anonymous

e is eulers number, its a constant just solve for k in $\large1500=3500e^{3k}$

21. anonymous

Oh ok. So i would have to divide each side by 3500 right? That would give me 3/7 = e^3k. Then take the inverse of each side which would give me In(3/7) = 3k right?

22. anonymous

Yep, now divide by 3

23. anonymous

ln(3/7)/3=k now you know k, plug it back in along with the time you want to know which is 9.5 $f(t)=3500e^{(\ln(3/7)/3)9.5}$

24. anonymous

So is that my final answer? Or do i have to solve more of it?

25. anonymous

@CalebBeavers

26. anonymous

@CalebBeavers I dont want to bug you, but i have to log off soon and i really need to know if thats my final answer or what more i have to do.

27. anonymous

My bad, i didnt even see the notification. if you plug the right hand side into a calculator it will give you the value of the boat after 9.5 years

28. anonymous

I did 3/7 = 0.42857142857142857142857142857143 then divided that by 3 and that equaled 0.14285714285714285714285714285714. Then i multiplied it by 9.5 and got 1.3571428571428571428571428571429. Then i pressed the In button and got 0.3053816495511818454864425669865. Is that right? Oh wait! Then do i do 3500e? The only thing is i dont see an e button on my calculator.

29. anonymous

You should plug it all in at once. use this calculator and type it in like 3500e^((ln(3/7)/3)*9.5)) http://web2.0calc.com/

30. anonymous

Im trying but its being stupid. Either that or im stupid. I typed it all in and it wont let me press the = sign. When i do press it, it wont solve it.

31. anonymous

Well it gives me 239.226

32. anonymous

Ok. Sorry. My computers stupid... lol Thanks for the help and being super patient!!!