Answer: $6297
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Step-by-step explanation:
x = number of years since the year 2000
eg: x = 1 represents the year 2001
y = value of the car in dollars
The point (x,y) = (0,29600) is on the curve and it's the y intercept. This is when Hailey bought the car with a value of $29600.
Another point on this curve is (7,12000) to indicate seven years have passed and the car is now worth $12000.
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Since the y intercept is 29600, this is the value of 'a' in the equation
y = a*b^x
Meaning we can update it to
y = 29600*b^x
Plug in the coordinates of the other point so we can solve for b
y = 29600*b^x
12000 = 29600*b^7
12000/29600 = b^7
b^7 = 12000/29600
b^7 = 0.405405
b = (0.405405)^(1/7)
b = 0.878991 approximately
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We found that
- a = 29600
- b = 0.878991 approximately
So we go from
y = a*b^x
to
y = 29600*0.878991^x
To verify this, plugging x = 0 should lead to y = 29600
Also, plugging in x = 7 should lead to y = 12000 or very close to it.
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The last step is to plug in x = 12 to find the car's value in 2012, i.e. x = 12 years after the year 2000.
So,
y = 29600*0.878991^x
y = 29600*0.878991^12
y = 6296.58182216087
y = 6297
The predicted car's value in 2007 is about $6297