1.The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold two cars (P₀=2). The second week the dealership sold nine cars (P₁=9).

a. Write the recursive formula for the number of cars sold,Pn.

b. Write the explicit formula for the number of cars sold,Pn.

c. If this trend continues, how many cars will be sold in the 4th week?

2.Starting in the year 2012, the number of speeding tickets issued each year in Middletown is predicted to grow according to an exponential growth model. During the year 2012, Middletown issued 200 speeding tickets (P₀=200). Every year thereafter, the number of speeding tickets issued is predicted to grow by 5%.

IfPndenotes the predicted number of speeding tickets during in a year after 2012:

a. Write the recursive formula forPn.

b. Write the explicit formula forPn.

c. If this trend continues, how many speeding tickets are predicted to be issued in 2030?

d. How long will it be until 1000 speeding tickets are issued in a year?

3.A population of 30 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 400 deer. Absent constraints, the population would grow by 30% per year.

a.Estimate the population after one year.

b.Estimate the population after two years.

c.Estimate the population after three years.