An article in Journal of Theoretical Biology [“Computer Model of Growth Cone Behavior and Neuronal Morphogenesis” (1995, Vol. 174(4), pp. 381–389)] developed a model for neuronal morphogenesis in which neuronal growth cones have a significant function in the development of the nervous system. This model assumes that the time interval between filopodium formation (a process in growth cone behavior) is exponentially distributed with a mean of 6 time units. Determine the following:

(a) Probability formation requires more than nine time units

(b) Probability formation occurs within six to seven time units

(c) Formation time exceeded with probability 0.9