Question 867252
Formulas and recipes are overrated.
0.55% ={{{0.55/100=0.0055}}}
The increase in population after the first year is {{{0.0055*P[0]}}} .
So the population goes from {{{P[0]}}} to
{{{P[0]+0.0055*P[0]=1.0055*P[0]}}} .
The population increases by the same {{{1.0055}}} factor every year.
After {{{t}}} years, the population is
{{{P(t)=P[0]*1.0055^t}}} .
You need to find the time {{{t}}} years after 2000, when {{{P(t)=350million}}} ,
knowing that in 2000, the population is {{{P[0]=250million}}}
{{{350million=250million*1.0055^t}}}
{{{350million/"250 million" =1.0055^t}}}
{{{7/5 =1.0055^t}}} or {{{1.4=1.0055^t}}}
Taking logarithms on both sides of the equal sign
{{{log(1.4)=log(1.0055^t)}}}
{{{log(1.4)=t*log(1.0055)}}}
{{{t=log(1.4)/log(1.0055)}}}
That yields {{{t=61}}} (rounded to nthe nearest integer.
So the population reaches 350million 61 years after 2000,
in the year 2061.
 
NOTE:
Since {{{1.0055=e^ln(1.0055)}}}<-->{{{1.0055^t=(e^ln(1.0055))^t=e^(t*ln(1.0055))}}} ,
and math teachers really like the irrational number {{{e}}} ,
they often write the function as
{{{P(t)=P[0]*e^(t*ln(1.0055))}}} .
It is really the same thing.