Question 978605
P=Po{1+r}^1.5  ;;time is in hours. You could use minutes, but hours is what is desired and it makes the exponent smaller.

P/Po=2 (doubling); Po=160
2=(1+r)^1.5
ln2 =1.5 * ln (1+r)

0.693=1.5 *ln (1+r); divide by 1.5 both sides
0.462=ln (1+r); raise both to e power

1.5872=(1+r)
r=0.5872


After t hours, the population, P=160 (1.5872)^t

Check.  After 3 hours, the population has doubled twice or increased 4 times.

P=160 (1+r)^3=160(1.5872)^3

1.5872^3= 3.998, or 4 by rounding.
P=160*4=640.  That is quadrupling.

After 24 hours, the population has increased by 1440/90 or 16 doubling times or by a factor of 2^16
2^16=65536

P=160(1+ 0.5872)^24
1.5872^24=65537, which is by rounding, very close to 65536, and that is 2^16
P=160*65536=10,485,760