Statistics and Probability

1 The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The firstweek the dealership sold two cars [P9 = 21 The second week the dealership sold six cars (P; = 6). Write the recursive formula for the number of cars sold. P", in the in + 1"\" week. Pn=Pn_1+ a Write the explicit formula forthe number of cars sold. P... In the In + nth week. If this trend continues, how many cars will be sold in the fourth week? A population of beetles are growing according to a linear growth model The initial population {week 0) is Po 2 4. and the population after lOweeks Is Pm : 94. Find an explicit formula for the beetle population after I: weeks. After how many weeks will the beetle population reach 202? A city currently has 131 streetlights. As part ofa urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks. How many streedlghis will the city have at the end of 42 weeks? Consider a population that grows according to the recursive rule Pn = P,I -1 + 95, with Initial population R; = 40. Then: P]: I)\": Find an explicit formula for the population. Yourformula should Involve u [use lowercase n) l Use your explicit formula to find Pm; l The sequence if\") is generated using the Fibonacci recursion rule fi+l = In + Ifnl and starts with the initial values of fa : 5 and f1 : 3. (Note. this indicates how the sequence is Indexed.) What are the next values In this sequence: 3': =