Part A Theory The equation for the logistic model is y= C where A, b and Care positive constants. 1+ Me In this section the relationships between the important features of the logistic graph and the constants A, b and C will be investigated. (a) Draw the graph of any logistic function with A, b and Cas positive constants and show all of its important features with an explanation of the method used to determine these features. (b) (i) Select the graphs of 5 logistic functions of your choice where A and b remain constant (A = 2. b = 0.5) but the value of C changes. Function 1 2 3 4 5 Equation A b C Equation of asymptote ii) Copy and complete the table. (iii) Use this table to explain the relationship between C and the asymptote. (c) (i) Select 5 logistic functions of your choice where b and C remain constant but the value of A changes. Function 1 2 3 4 5 Equation A b C * value of point of inflection # value of point of inflection (ii) Copy and complete the table. (iii) Use this table to explain the relationship between C and the y value of the point of inflection. (iv) Use modelling techniques to find the relationship between A and the r value of the point of inflection. Discuss the accuracy of your result. (v) Explain the meaning of the term reciprocal and give 3 examples. How does this term relate to the value of b and the / value of the point of inflection? (d) (i) Use your result in part (c) (v), algebraic techniques and laws of logarithms to show that your result in part (c) (iii) is correct. Use one of your equations from the table. (ii) Use your result from part (c) (iii), algebraic techniques and laws of logarithms to show your result in part(c) (v) is correct. Use one of the equations from your table. (iii) Now, write down the general rule for finding the / coordinate of the point of inflection for any logistic function y= C