In 2003, the price of a certain automobile was approximately 32,600 with a depreciation of 2,060 per year. After how many years will the car's value be 18,180 a) Write an equation to model the problem Let t represent the number of years after 2003. For example, the year 2005 would be represented by t =2. Answer: 18180 b) Colvo tho oquation to find the answer to the question above (Note Include the units, in this case years.)

a) To write an equation to model the problem, we need to consider the initial value of the car and the rate of depreciation. The initial value of the car in 2003 is $32,600, and it depreciates by $2,060 each year. Let $t$ represent the number of years after 2003. The value of the car after $t$ years can be represented by the equation:<br /><br />\[ V = 32600 - 2060t \]<br /><br />where $V$ is the value of the car after $t$ years.<br /><br />b) To find the number of years after which the car's value will be $18,180, we need to solve the equation for $t$ when $V = 18180$:<br /><br />\[ 18180 = 32600 - 2060t \]<br /><br />Now, let's solve for $t$:<br /><br />\[ 2060t = 32600 - 18180 \]<br />\[ 2060t = 14420 \]<br />\[ t = \frac{14420}{2060} \]<br />\[ t = 7 \]<br /><br />So, the car's value will be $18,180 after 7 years.