35,000+ 30,000 25,000- 20,000- Value of Car 15,000- 10,000- 5,000 10 Years Since Purchase Given the graph of the exponential equation of a is the equation for the the graph goes through the points (0, 30000) and (1, 22500) point y=30,000( t t )^ *; y = 0.75 * (30000) deg; y=22,500( 4 2 )^ *; n = 30 * (4) ^ 2
The equation for the graph based on the given points can be determined using exponential decay.
Given the points (0, 30000) and (1, 22500), we can use the general form of the exponential decay equation:
y = a * (b) ^ t
where:
- y represents the value of the car at time t
- a represents the initial value of the car
- b represents the decay factor
- t represents the time since purchase
Substituting the first point (0, 30000) into the equation, we get:
30000 = a * (b) ^ 0
30000 = a
So, the initial value of the car (a) is 30000.
Substituting the second point (1, 22500) into the equation, we get:
22500 = 30000 * (b) ^ 1
22500 = 30000b
Simplifying the equation, we find:
b = 22500 / 30000
b = 0.75
So, the equation for the graph is:
y = 30000 * (0.75) ^ t
Therefore, the equation is y = 30000 * (0.75) ^ t.