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The population of a city is observed as growing exponentially according to the function P(t) = P0ekt, where the population doubled in the first 50 years.
(a) Find k to three decimal places.
(b) By what factor (to two decimal places) will the original population have grown in the first 125 years?
(c) When will the original size of the population have grown by a factor of ten?
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
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of all those survey 390 were under 18 years of age if 20%were 18, how many responded to the survey
Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
Mod(Z-25i) Sol) mod (Z-25i) means Z lies in the circumference of the circle with (0,25) at its centre and radius less then 15. so difference in the max and min value of arg Z is
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
What are square roots
1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon): S ---> bB | aSS A ---> aB | bAA B ---> E | bA | aS a. D
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Determine whether R is an equivalence relation or a p
Q. Difference between Probability and statistics? Ans. Probability and statistics are used in many different aspects of life. What are they and why are they so popular?
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