Question

The exponential decay graph shows the expected depreciation for a new boat, selling for $3,500, over 10 years.



Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.

Answer 1

@satellite73 @Hero @jim_thompson5910 @hartnn Please help!

Answer 2

Exponential functions have the form: \[
ab^t+c
\]Where \(c\) is where it converges (in this case 0), \(a\) is the initial value ($3,500), and \(b\) is the factor by which it decreases after one unit of time.

Answer 3

okay.. so can you help me out on writing the exponential function?

Answer 4

We need to solve for \(b\). It looks like when t is 2, we'll be close to 2000 \[
\begin{array}
2000 &=& 3500b^2 \\
\frac{4}{7} &=& b^2 \\
b &=& \sqrt{\frac{4}{7}}
\end{array}
\]

Answer 5

Why did you use 3 0's?

Answer 6

Its \(2000\) it cut it off

Answer 7

ok so 200=3500b^2 is my exponential function for the graph to strat with?

Answer 8

2000*

Answer 9

start*

Answer 10

no

Answer 11

Read what I said a few times

Answer 12

what is t? Do I need to find that?

Answer 13

No, t, is the input of the function.

Answer 14

I'm sorry, but I'm really confused :(... So my equation is gonna be what ab^t+c when I plug in the numbers?

Answer 15

Basically

Answer 16

i don't think there is a \(c\) in this

Answer 17

you can use a base of \(\sqrt{\frac{2000}{3500}}=\sqrt{\frac{4}{7}}\) if you like because it looks like it goes from 3500 to 2000 in two years, or else you can use
\[3500\times \left(\frac{4}{7}\right)^{\frac{t}{2}}\] since it takes two years to decrease by \(\frac{4}{7}\)

Answer 18

to answer the second part, replace \(t\) by \(9.5\)