Question 313805
A certain country's population P(t), in millions, t years after 1980 can be approximated by
P(t) = 5.495(1.016)t .
In what year did the country's population reach 3 million?
a.1947
b.1932
c.1942
d.1952 
.
Given:
{{{ P(t) = 5.495(1.016)^t }}}
Set P(t) to 3 and solve for t:
{{{ 3 = 5.495(1.016)^t }}}
{{{ 3/5.495 = (1.016)^t }}}
{{{ log(1.016,(3/5.495)) = t }}}
{{{ log(3/5.495)/log(1.016) = t }}}
{{{ -38.13 = t }}}
.
1980-38.13 = 1941.87 = 1942
Answer is c