directions: show all work, and answer each question that is asked. explanations should be given in complete sentences. all graphs should be drawn accurately on this sheet, and be fully labeled. write your final answers in the boxes provided, when possible.

according to the us census bureau, the population of the us in the year 2000 was 281,421,906 people. in the year 2010, it was 308,745,538 people. the population was growing steadily during this period.
use this information to express the us population as a function of time since the year 2000. use t=0 to represent the year 2000.
p(t)=

b. what would this model indicate that the us population was in the year 2005? (the actual population in that year was 296,507,061.)

c. what would this model indicate is the year in which the population surpasses 400 million people?

2.) a solar water heater costs about $6120 to install (after rebates). a traditional gas water heater costs about $800, and costs about $350 per year to run. the average annual cost to run the solar water heater is about $70.

a. create total cost functions for each of the water heaters as a function of the number of years that it is used.

gas water heater cost solar water heater cost

g(t)= s(t)=

b. graph these functions on the same set of axes.

c. how many years would you need to use a solar water heater in order for the total cost to become less than the total cost of the gas water heater? answer below, and label the point on the graph.