Given the graph of the exponential equation representing the value of a car since purchase, which option is the correct exponential equation for the graph if the graph goes through the points (0,30000) and (1,22500)?
To solve this problem, we can use the general form of an exponential equation:
y = a * b^x
where:
- y is the value of the car
- x is the number of years since purchase
- a is the initial value of the car (when x = 0)
- b is the growth/decay factor
We are given two points: (0, 30000) and (1, 22500).
Using the point (0, 30000), we can substitute these values into the equation:
30000 = a * b^0
30000 = a * 1
30000 = a
So, we have found that a = 30000.
Using the point (1, 22500), we can substitute these values into the equation and solve for b:
22500 = 30000 * b^1
22500 = 30000 * b
b = 22500 / 30000
b = 0.75
Now we have determined the values of a and b, so we can write the exponential equation:
y = 30000 * (0.75)^x
Therefore, the correct exponential equation for the graph is y = 30000 * (0.75)^x.