statistics and Probability

6 Starting In the year 2012, the number of speeding tlckets isued each year In Mlddletown is predicted to grow according to an exponential growth model. During the year 201?. Middletown Issued 190 speeding tickets (Pa = 190). Every year thereafter, the number of speeding tickets issued Is predicted to grow by 10%. If P" denotes the predicted number of speeding tickets during the year 2012 + rt then Write the recursive formula for P,I Pn=:]x Pail Write the explicit formula for P. If this trend continues, how many speeding ticketsare predicted to be issued in 2031? D tlckets Assume there Is a certain population of sh in a pond whose growth ls described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 sh. Absent constraints. the population would grow by 250% per year. lfthe starting population Is given by pa : 300. then after one breeding season the population of the pond ls given by me: After two breeding seasons the population of the pond is given by w: A population of 50 deer are Introduced into awildlife sanctuary. It Is estimated that the sanctuary can sustain up to 500 deer. Absent constraints, the population would grow by 2096 per year. Estimate the population after one year w: Estimate the population after two years a = :1 Suppose 17 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 80% a month. If the yard can only sustain 140 plants. use a logistic growth model to estimate the number of plants after 2 months. Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 30% a year. If the lake can sustain a maximum of 2600 trout, use a logistic growth model to estimate the number of trout after 3 years. Let P(t) : zoomum)' be the population of a town t years after the year 2000. Estimate in which year the population will reach 27056