Question 1193500
<br>
Here is a logistic growth formula:<br>
{{{f(x)=L/(1+a*e^(-bt))}}}<br>
L is the carrying capacity, given as 70.<br>
a and b are constants to be determined from the given information.<br>
The initial population, f(0), is 30:<br>
{{{f(0)=70/(1+a*e^0)=70/(1+a)=30}}}
{{{70=30(1+a)=30+30a}}}
{{{40=30a}}}
{{{a=40/30=4/3}}}<br>
The population increases by 50% each month, so the population after one month is 1.5(30)=45:<br>
{{{45=70/(1+(4/3)e^((-b(1))))}}}
{{{70=45(1+(4/3)e^(-b))}}}
{{{70=45+60e^(-b)}}}
{{{25=60e^(-b)}}}
{{{e^(-b)=25/60=5/12}}}
{{{-b=ln(5/12)}}} =-0.87547 to 5 decimal places
{{{b=0.87547}}}<br>
{{{f(n)=70/(1+(4/3)e^((-0.87547)n))}}}<br>
That function gives the following populations after n months to fill your chart:<br><pre>
  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</pre>