In 2000 the population of a city was 69000 The population ha

In 2000, the population of a city was 69,000. The population had grown to 99,000 by 2010. If the population grows by the same percent each year, when will the population reach 178,000? Report the number of years after 2000. The population will reach 178.000 about years after 2000. If necessary, round to the two decimal places. Do not include units.

Solution

We have to use the following formula

P(t)=P(0)e^rt

99000=69000e^10r

99/69=e^10r

taking ln on both sides

ln(99/69) =10r

r=.036

178000=69000e^{.036 t}

178/69=e^.036t

Taking ln on both sides

ln(178/69)=.036t

t=26.25 yrs

.157/10=1+r