## swiftskier96 Group Title Help!?!?!?!?!?!? 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. Show your work. one year ago one year ago

1. swiftskier96 Group Title

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. Show your work.

2. binarymimic Group Title

oh. well the initial value is 3500 and it looks like at t = 2 the value is 2000 try setting up a general exponential function like \[N = N _{0}e^{kt}\]

3. binarymimic Group Title

where N0 is the initial value, N is the present value, k is a constant, and t is the time

4. swiftskier96 Group Title

So the initial value would be 3500, the present value is 2000, im not sure what k is, and t is 9.5 years? @binarymimic

5. swiftskier96 Group Title

What is k? @binarymimic

6. binarymimic Group Title

you'd have to solve for it by letting N0 = 3500, N = 2000, and t = 2

7. binarymimic Group Title

because at t = 2, the present value is 2000 hence 2000 = 3500e^(k*2) when you get a value for k it will be negative, and try to round it to at least 5 digits for accuracy

8. swiftskier96 Group Title

Ohhh ok. I see. Thank you! :)

9. binarymimic Group Title

sure. and when you get the value of k then you can write out the general equation and let t = 9.5

10. swiftskier96 Group Title

Then do i add the answers together or something? Cause then ill have k = ? and k = ?.

11. binarymimic Group Title

not sure what you mean but when you solve for k, then you'll use that k in the equation \[N = 3500e ^{k * 9.5}\] to solve for the present value at time t = 9.5