Answer :
Given:
The initial value of the car = $75,700
Decreasing rate = 4.3%
To find:
The value of r in the exponential DECAY formula.
Solution:
The exponential decay formula is:
[tex]y=a(1-r)^t[/tex]
Where, a is the initial value, r is the rate of decay on decimal and t is the time period.
The initial value of the car is $75,700 and its value decreases 4.3% annually. So,
[tex]a=75,700[/tex]
[tex]r=\dfrac{4.3}{100}[/tex]
[tex]r=0.043[/tex]
The required exponential decay formula is:
[tex]y=75,700(1-0.043)^t[/tex]
Therefore, the value of r in the exponential decay formula is 0.043.