The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 7.1 % per hour. how many hours does it take for the size of the sample to double?

Double
from initial amont of P to final amount of 2P
so

2P=P(1.071)^time
divide both sides by P
2=1.071^time
take the ln of both sides
ln2=timeln1.071
divide both sides by ln 1.071
(ln2)/(ln1.071)=time needed
using calculator
10.1052=time needed
about 10.1 hours