SOLUTION: MAT 145: Topics In Contemporary Math 20: Logistic Growth 1) The population of fuzzy quadrupeds increases by 50%) every month after they are introduced to a new

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Question 1193500: MAT 145: Topics In Contemporary Math

20: Logistic Growth
1) The population of fuzzy quadrupeds increases by 50%) every month after they are
introduced to a new region. Suppose 30 fuzzy quadrupeds are accidentally introduced to
Springfield when a family visited the region to which fuzzy quadrupeds are native.
However, Springfield only has a carrying capacity of 70 fuzzy quadrupeds. How many
fuzzy quadrupeds would there be for each of the first five months after they were
introduced to the new region?
this is a chart below:
Month Formula Population size
0 Beginning population
1
2
3
4
5
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

How far below is the chart with the formula ?

And why don't YOU use this formula to complete the assignment ?


Do you afraid to get your hands dirty?



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It appears more tutors are tired of seeing
MAT 145: Topics In Contemporary Math

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a logistic growth formula:

f%28x%29=L%2F%281%2Ba%2Ae%5E%28-bt%29%29

L is the carrying capacity, given as 70.

a and b are constants to be determined from the given information.

The initial population, f(0), is 30:

f%280%29=70%2F%281%2Ba%2Ae%5E0%29=70%2F%281%2Ba%29=30
70=30%281%2Ba%29=30%2B30a
40=30a
a=40%2F30=4%2F3

The population increases by 50% each month, so the population after one month is 1.5(30)=45:

45=70%2F%281%2B%284%2F3%29e%5E%28%28-b%281%29%29%29%29
70=45%281%2B%284%2F3%29e%5E%28-b%29%29
70=45%2B60e%5E%28-b%29
25=60e%5E%28-b%29
e%5E%28-b%29=25%2F60=5%2F12
-b=ln%285%2F12%29 =-0.87547 to 5 decimal places
b=0.87547

f%28n%29=70%2F%281%2B%284%2F3%29e%5E%28%28-0.87547%29n%29%29

That function gives the following populations after n months to fill your chart:
  months   population  (rounded)
 -------------------------------
    0      30             30
    1      45             45
    2      56.842         57
    3      63.842         64
    4      67.296         67
    5      68.847         69
    .
    .
    .
   10      69.985         70