Question

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

Answer 1

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

Answer 2

There's two variables...

Answer 3

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

Answer 4

Hmm, start off by dividing both sides by 3500

Answer 5

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

Answer 6

Yeah, now take natural log of both sides

Answer 7

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

Answer 8

Yep, now just divide by 9.5

Answer 9

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

Answer 10

Yep =D

Answer 11

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?

Answer 12

so it gives you the function

N = 3,500e^(kt)

?

Answer 13

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

Answer 14

Hmmm. lets start over

whats the original question and all the information it gives you?

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

We need to solve for e?

Answer 20

e is eulers number, its a constant

just solve for k in

\[\large1500=3500e^{3k}\]

Answer 21

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?

Answer 22

Yep, now divide by 3

Answer 23

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

\[f(t)=3500e^{(\ln(3/7)/3)9.5}\]

Answer 24

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

Answer 25

@CalebBeavers

Answer 26

@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.

Answer 27

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

Answer 28

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.

Answer 29

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/

Answer 30

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.

Answer 31

Well it gives me 239.226

Answer 32

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