The logistic equation has been used to model the spread of technology. let n∗ be the number of ranchers in uruguay, and n(t) the number who have adopted a new pasture technology. the rate of adoption dn/dt is proportional to the number who have adopted the technology, and the fraction who have not (and thus are susceptible to changing). so the equation is dn dt = αn 1 − n n∗ according to a study by banks (1993), n∗ = 17, 015, n(0) = 141, α = 0.49 per year. determine how long it takes for the new technology to be adopted by 80% of the population of ranchers.