Populations growing multiplicatively with constant r have a constant doubling ti
ID: 90935 • Letter: P
Question
Populations growing multiplicatively with constant r have a constant doubling time Yellow star-thistle (Centaurea solstitialis) is a spiny annual plant native to the Mediterranean region. The species has invaded several regions of the United States. It is a noxious weed that is unpalatable to livestock (including American bison). Jane, the rancher, discovers that 1 hectare of her 128-hectare pasture has been invaded by star-thistle. A year later, she finds that the weed population has grown to cover 2 hectares. 1. Based on the information above, how many hectares do you predict the star-thistle population will cover in 1, 2, and 3 more years if the population is growing additively by a constant number? How many hectares if the population is growing multiplicatively with constant r? 2. Imagine that Jane discovers the star-thistle population only after it has already covered 32 hectares of her pasture. How many years does she have until the weed completely covers the pasture if its population is growing additively by a constant number each year? How many years does she have if it is growing multiplicatively with constant r? The invasive yellow star-thistle is noxious to grazing livestock.Explanation / Answer
1. If the population growing additively then after each more year result in additive increase in hectare growth i.e 3, 4 and 5 after 1, 2 and 3 more years.
if population growing multiplicately then each year it doubles there fore it covers 4, 8 and 16 hectare after 1, 2 and 3 more years.
1. for additively since each year it cover 1 hectare there fore it will take 32-5 = 27 more years to covered 32 hectare ( total 32 years).
however in case of multiplicately it doubless each year thus it covered 32 hectares in six years.