According to Hooke's law for springs, developed by Robert Hooke (1635-1703), the force exerted by a spring that has been compressed to a length x is given by the formula F = −k(x − x0), where x0 is the natural length of the spring and k is a constant, called the spring constant. A certain spring exerts a force of 32 lb when compressed to a length of 2 ft and a force of 16 lb when compressed to a length of 3 ft. For this spring, find the following.
a. The linear equation that relates the force exerted to the length compressed
b. The spring constant
c. The natural length of the spring