First you need to calculate the growth factor. You can do this by sett up 2 equations from the given information
500 = A(r^20)
1100 = A(r^30) divide the second equation by the first and A drops out and leaves you with
2.2 = r^10 take the 10th root of both sides to solve for r= 1.082./minute
Now substitute 1.082 for r in either equation to solve for A(Initial Value)
500=A(1.082^20). A= 500/1.082^20= 103.377
For the doubling period the ratio of the final to the initial value is 2 so
2= 1.082^t take the natural log of both sides( need to free up the variable t
ln 2 = ln1.082^t by rules of logs this converts to t(ln1.082)
t = ln2/ln1.082 = 8.759 minutes
To find the population at 95 minutes solve y= 103.377(1.082^95)= 184,507
To solve for when population will reach 13000 solve 13000= 103.377(1.082^t)
1.082^t= 13000/103.377
1.082^t = 125.753
t ln 1.082= ln 125.753
t=ln125.753/ln1.082 = 61.34 minutes
