The value of an antique car is modeled by the function v(x)=107,000(1.009)^
(2/3x) where x is the number of years since 2005. by what approximate percent rate is the value of the car increasing per year?

To get a percent rate, let the value of the car based on two consecutive years. The variable x represents a year. You can set any two numbers of year as long as they are consecutive; say x = 0 and x = 1.

Use the calculator to get instantly the values of V(x).
For V(x = 0)
V(x = 0) = 107,000(1.009)^[2/3(0)] = 107,000

For V(x = 1)
V(x - 1) = 107,000(1.009)^[2/3(1)] = 107,641

Another way of getting the percentage between two values is called the "relative change."
(107,641 - 107,000) / 107,000 = 0.0060 = 0.60%

Answer is either b or c