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)?

Answer 1

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.