Question

ECOLOGY POPULATION GROWTH

Show your work!!

D. Population of Houston Area Census Date Population 1850 18,632 1860 35,442 1880 1890 1900 1910 1920 1930455,570 49.986 71,316 86,224 134,600 185,654 272,475 1940 1950 1960 1,430,394 1970 1,999,316 646,869 947,500 1980 2,905,334 If a population is growing exponentially, it will take the same amount of time for the population to double, regardless of the size of the population (e.g. if it is growing exponentially, it will take the same amount of time to go from 2 to 4 or from 2000 to 4000) Approximately how long did it take the population of Houston to double from 35,000 to 70,000? How long did it take to double again from 70,000 to 140,000? How long did it take to double from 1 million to 2 million? Do the doubling times of the Houston population support the assumption of exponential growth? If a population is growing exponentially (N-Noet with r remaining the same), then the natural log of the population size will be a linear function of t (In(N) -rt+ c where c is a constant). What does the slope of the line represent? Plot the natural log of Houton's population over time (on another sheet of paper), If the result is linear, than the population is growing exponentially Is the population growing exponentially according to this calculation?

Answer 1

Population of Houston was roughly 35,000 in 1860, and it became 70,000(roughly) in1880. So this took 1880-1860=20 years.

The population was roughly 140,000 in 1900. So, going from 70,000 to 140,000 it took approximately 1900-1880=20 years.

The population was about 1 million in 1950 and rose to 2 million in 1970. This took 1970-1950=20 years.

From the 3 figures we calculated above the assumption of exponential growth has not been violated.

Slope of the line(r) denotes the per capita rate of increase –that is, how quickly the population grows per individual that are present in the population.

The plot:

                              

14 으12 10 1860 1880 1900 1920 19401960 1980 Year

The relationship is approximately linear, but it is clearly not exact. So, the population is approximately rowing exponentially.