bmartinez26
10.03.2020 •
Mathematics
In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponentially, doubling every 6 months.
a. Determine P(t), the function that gives the population at time t, and the differential equation describing the population growth.
b. After how many years, rounded to one digit after the decimal point, did the rabbit population reach 1,000,000?
c. Determine the rate of population change, in rabbits/year, midway through the third year. (Warning: t is not 3.5, just like the year midway through the 21st century is not 2150.) Round the final answer to 2 digits after the decimal point.
Solved
Show answers
More tips
- C Computers and Internet How Do You Refill Cartridges?...
- F Family and Home How to Keep Your Home Warm: Tips and Tricks...
- D Dating, Love, Relationships Does a Person s Character Depend on the Color of Their Eyes?...
- O Other Childhood Fears: What Many of Us Experienced...
- H Health and Medicine Simple and Effective: How to Get Rid of Cracked Heels...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
Answers on questions: Mathematics
- M Mathematics Which quadrant is negative 3 and positive 15...
- M Mathematics SOMEONE HELP ME PLEASE...
- E English What limits population growth in puerto rico? give a few examples 20 points!!...
- M Mathematics Alex has a grid in the shape of a rectangle. he has right triangles. each right triangle has an area of 25 square millimeters and each right triangle fits on the grid. if the...
- H History Actinobacteria sp. are organisms called chemoorganohetereotrophs. they do not use oxygen to breathe. they break down organic material and convert it to inorganic material. which...
- S Social Studies Why did men sign up for war 1...
- E English I have this sentence. “He shuddered, sinking deeper into the ( ) of his bed. I just can’t come up with the word I’m looking for. I kinda mean like the seams or cracks but that...
Ответ:
a) P' = P
where t is step of 6 months
b) 7.7 years
c)1064.67 rabbits/year
Step-by-step explanation:
The differential equation describing the population growth is
Where t is the range of 6 months, or half of a year.
P(t) would have the form of
where is the initial population
After 6 month (t = 1), the population is doubled to 48
Therefore
where t is step of 6 months
b. We can solve for t to get how long it takes to get to a population of 1,000,000:
So it would take 15.35 * 0.5 = 7.7 years to reach 1000000
c.
We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48
Therefore,
At the mid of the 3rd year, where t = 2.5, we can calculate P'
rabbits/year
Ответ: