solving logarithm word problems

Question

The number of victuims of a flu epidemic s increasing at a rate of 7.5% per week. If 20,000 persons are currently infected, find in how many days we can expect 45,000 to have the flu. Use y=y0e^0.075t and round to the nearest victim.

Answer 1

The growth in numbers of victims is 45000/20000=9/4=2.25, therefore 2.25=e^0.075t, where t is in weeks.

ln(2.25)=0.075t, so t=ln(2.25)/0.075=10.81 weeks=10 weeks 6 days approx. or about 76 days.