LOGISTIC FUNCTIONS f (x) = There are many situations in the world from rates of chemical l + e'x'xo) reactions, to population growth, to cumulative spread of viruses x\" = \"all\": of midpoint and vaccination, to the diffusion of an idea, to economics, or to L = maximum value crop production which can be modelled with the logistic function. A: = growth rate You may use your values in all of the following problems. L MY VALUES 6. Create a graph of your function clearly showing the end behaviour and behavior near x = x0. 7. Calculate the y-intercept of your logistic function and write the result as a coordinate. An extremely small value is acceptable, but you must report at least one significant figure. 8. Justify and show that for your function with your values each of the following statements are true. .1111; fix) = 0 flare) = % game. flm) = L OT 01" oacc> oo,f(:.c)>O cases>00, f(x)>L 9. With your function determine the values of x that satisfy the following inequality; flz) : % 10. Calculate the W for your function on the interval x E [7. 8]. 11. Derive yourself, or prove algebraically, that the inverse of the logistic function f (x) can be written as; rice) : in?) _ ln(Lk a) + $0