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

Mathematics
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How do you solve this?? N = 3,500e^(k * 9.5)
There's two variables...
I know. Im supposed to solve for k. Does that help at least a little bit? @CalebBeavers

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Hmm, start off by dividing both sides by 3500
So it would be N/3,500 = e^9.5k? @CalebBeavers
Yeah, now take natural log of both sides
So In(N/3,500) = 9.5k?
Yep, now just divide by 9.5
So In(N/3,500)/9.5 = k?
Yep =D
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?
so it gives you the function N = 3,500e^(kt) ?
Well it didnt give me that but i asked the question earlier and someone said to use that equation.
Hmmm. lets start over whats the original question and all the information it gives you?
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
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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
So if i plugged in 9.5 it would look like 1500 = 3500e^(3 * 9.5)?
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
We need to solve for e?
e is eulers number, its a constant just solve for k in \[\large1500=3500e^{3k}\]
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?
Yep, now divide by 3
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 \[f(t)=3500e^{(\ln(3/7)/3)9.5}\]
So is that my final answer? Or do i have to solve more of it?
@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.
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
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.
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/
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.
Well it gives me 239.226
Ok. Sorry. My computers stupid... lol Thanks for the help and being super patient!!!

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