Johnnie begins a regullar walking program as a art of his new exercise routine. The first week he walks a distance of 5 km, 8 km the second week, 11 km the third week, 14 km the fourth week and so on for a period of 12 weeks. How far will Johnnie walk during the 12th week?

a) Explain why this sequence is an arithmetic sequence.

b) Write out the sequence using blanks where appropriate.

c) Write the explicit formula for the sequence.

d) How far will the patient walk during the 12th week?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?