A new car worth $20,000 loses 20% of its value every year. Is the value of the car represented by a linear or exponential function?

Exponential.

One way to think about this, is to ask how much you will lose each year. The first year you're losing 20% of $20,000 ($4,000). The second year you're losing 20% of 16,000 ($3,200). The dollar value your car loses each year diminishes exponentially, so it is not a linear but an exponential function.