The concentration of E. coli bacteria in a swimming area of a lake is monitored after a rainstorm where time is the hours after the storm ended and CFU is a 'colony-forming unit' as shown: 4 8 12 16 Time (hr) C (CFU/100mL) 1600 1320 1000 890 20 650 24 560 Based on the initial data we propose an exponential model: C = a) Linearize the model, fit a straight best-fit line, and back transform the model (report the a1 and b1 parameters). b) Use your back-transformed model to define a function that can estimate the concentration of E. Coli when given a time in hours after the storm ended. Use your defined model to estimate the bacterial concentration at time =0 (right when the storm ended). c) Using your exponential model, predict when the bacterial concentration will reach 200 CFU/mL. d) Plot the data and the back transformed model. a₁e¹₁*t

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Concept of Randomized Approximation Algorithms

Randomized algorithms are algorithms that use random numbers to determine what to do next at any point in their logic. This means that it uses randomization for operation in the logic. Due to this randomness, the time and space complexity of the standard algorithm is reduced.