Using the linear congruential random number generator determine the first five random numbers given that: ,
,
, and
. Transform these random numbers to lie between 0 and
The linear congruential generator (LCG) is defined by the formula: [ x_{n+1} = (a x_n + c) \mod m ] Given: [ x_0 = 27, \quad a = 17, \quad c = 43, \quad m = 100 ] Step 1: Calculate (x_1) [ x_1 = (17 \cdot 27 + 43) \mod 100 _______ ________ _________ _________ ____.
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Use the Secant method with initial guesses of and
to calculate the root/s of the equation
up to three iterations. Calculate the absolute relative approximate error at each stage.
A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :
| x (time in hours) | 0 | 4 | 8 | 12 | 16 | 20 | 24 |
| y | 25 | 36 | 52 | 68 | 85 | 104 | 142 |
What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method?
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Derive the Runge-Kutta 2nd Order formula for the differential equation
Using the linear congruential random number generator determine the first five random numbers given that: ,
,
, and
. Transform these random numbers to lie between 0 and
Calculate the first derivative of the function at
using the forward divided difference, backward divided difference and central divided difference methods with a step size of
rad. Also calculate the absolute true error in each case.