The Gompertz growth model is commonly used to model tumor cell growth. Let v(t) be the tumors volume, then dvt dt et vt where and are two appropriate constants (EdelsteinKeshet, 2005). a. Verify that the solution to this equation is given by vt v0e =1et , where v0 is the initial tumor volume. b. This model takes into account the fact that when nutrients and oxygen are scarce at the tumors core, its growth is impaired. Find the final predicted tumor volume (let t ). c. For a specific mouse tumor, it was experimentally found that 2:5 days; 0:1 days with v0 50 103 mm3 (Chignola, 2005). Use any method available to make a plot of v(t) vs. t. d. Check the result obtained in Part b with the results from the graph found in Part c.

CS 064 Notes 02/09/16 Tauntology- something that’s always true Ex. x ∨¬ x, by theorem 7.2 (x ∨¬ x ) ∧(y y) =T ∧( y y) ; by Theorem 7.2 (x ∨¬ x) =T ∧(¬ y ∨ y) ; by proposition 7.3 (x y¬= x ∨ y) = T ∧( y ∨¬ y) ; by commutative property of ∨ =T∧T ; by Theorem 7.2 (x ∨ ¬ x) = T ; definition of ∧ Theorem 8.6: The number of lists of length k, where elements are chosen krom a pool of n possible elements: o n if repetitions are allowed o n (k)f repetitions are not allowed, where(k)=(n-1)*(n-2)*(n-3)*(n- 4)…*(n-(k-1)) ex. arranging tiles A, B, C, D, E, F, G 7*6*5*4*3*2*1 0 1 2 3 4