Given the graph of the exponential equation representing the value of a car since purchase, which option is correct exponential for the graph if the graph goes through the point (0, 30000) and (1, 22500)?
A. y = 30,000(4/3)^x
B. y = 22,500(3/4)^x
C. y = 0.75(30,000)^x
D. y = 30,000(3/4)^x
To find the exponential equation that represents the value of the car, we can use the general form: y = ab^x, where a is the initial value and b is the growth/decay factor.
We are given that the graph goes through the point (0, 30000). Plugging this into the equation, we get:
30000 = ab^0
30000 = a
Therefore, we know that the initial value is 30000.
We are also given that the graph goes through the point (1, 22500). Plugging this into the equation, we get:
22500 = 30000b^1
22500 = 30000b
b = 22500/30000
b = 3/4
Therefore, the growth/decay factor is 3/4.
Substituting these values into the equation, we get:
y = 30000(3/4)^x
Therefore, the correct option is D. y = 30,000(3/4)^x.