Answer:
The rate of decay each month is -0.006924%
Step-by-step explanation:
The cost of a car after 1 year at a 8% decreased
Decreased price = Sale price - (Sale price x porcentage of decreased/100%)
Decreased price = $20,000 - ($20,000 x 8%/100%)
Decreased price = $20,000 - ($20,000 x 0.08)
Decreased price = $20,000 - $1,600 = $18,400
So, the value of the car decreased by 8% in a year is $18,400.
The general equation for exponential decay is:
Where
y = final amount
C = Sale price
r = rate of decay
t = time
We know that the sale price was $20,000. After a year the decreased price is $18,400.
From the general equation for exponential decay, our sale price is $20,000 decreased over a time of 12 months resulting the final amount of $18,400.
substituting the values
Solving the equation for r