Answer:
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.
