I've been struggling with this. i need asap. (anyone that's good in math.)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.

y = 3500(3/7 ) ^ 1/3

y = 239.23

Step-by-step explanation:

For exponential decay

y =a b^x

a = 3500

b<1

We can use the point (3, 1500)

1500 = 3500 * b^3

Divide each by 3500

1500/3500 = 3500/3500 b^3

15/35 = b^3

3/7 = b^3

Take the cube root of each side

(3/7) ^ 1/3 = b^3 ^ 1/3

b = (3/7 ) ^ 1/3

The function is

y = 3500 (3/7) ^ 1/3 x

We want to find y when x=9.5

y = 3500 (3/7) ^ (9.5 /3)

y = 3500 ( 3/7) ^ 3. 166666666

y = 3500 (.06835)

y = 239.23

Lets check a point and see if we a close

(7,500)

y = 3500 (3/7)^ (1/3*7)

y = 3500 (3/7) ^ (7/3)

y = 484.68

That is pretty close.  We do not know the exact value since we are reading from a graph.

c

step-by-step explanation:

step-by-step explanation: