Let N(d) be the number of asteroids of diameter ≤ d kilometers. Data suggest that the diameters are distributed according to a piecewise power law:

(a) Compute the number of asteroids with a diameter between 0.1 and 100 km.
(b) Using the approximation N(d + 1) − N(d) ≈ N (d), estimate the number of asteroids of diameter 50 km.

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N'(d) = 1.9 x 10ºd-2.3 2.6 x 10¹2d-4 for d < 70 for d≥ 70