Mark true or false and justify your answers. You can use either definition of bounds (limits or inequalities) to justify. Show your work. 2^n + 1 = O(2^n) e^x = O(x^10) x^10 = O(e^x) x^10 = O(e^x) x^3 + 3x^2 + 5x + 2 = theta (x^3) log^2 n = O(n) Solve the given recurrence relation using back substitution (plug and chug) or recurrence tree. Show your work: T(n) = 3T(n/3 + n, T(1) = 1 and n = 3^k A century plant is a plant that lives forever and reproduces only once in its lifetime. Each plant gives birth to two plants in its first year and then stops. Let T(n) be the number of century plants in the nth year, given T(1) = 1. Write a recurrence relation for T(n) and solve it using back substitution/recursion tree method