SOLUTION: 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?

Algebra ->  Expressions-with-variables -> SOLUTION: 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?       Log On


   

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
I can't do it backwards. Please help
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
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%28t%29+=+5.495%281.016%29%5Et+
Set P(t) to 3 and solve for t:
+3+=+5.495%281.016%29%5Et+
+3%2F5.495+=+%281.016%29%5Et+
+log%281.016%2C%283%2F5.495%29%29+=+t+
+log%283%2F5.495%29%2Flog%281.016%29+=+t+
+-38.13+=+t+
.
1980-38.13 = 1941.87 = 1942
Answer is c