Question

The population N(t) (in millions) of a country t years after 1980 may be approximated by the formula
N(t) = 205e0.0104t.
When will the population be twice what it was in 1980?

Answer 1

The formula is, \(\large\color{black}{N(t) = 205e^{0.0104t} }\)
However when will it be twice more than in 1980 depends on what the value of N(t) (or the present population) is.

Answer 2

This is all that was in the problem

Answer 3

well, let me show why I said what I said, and what I still hold.
\(\large\color{black}{ N(t)=205e^{0.0104t} }\)
hitting both sides with a natural log, (the ln)

\(\large\color{black}{ \ln(~N(t)~~)=\ln(~205e^{0.0104t} ~) }\)
exponent will go in front of the natural log,

\(\large\color{black}{ \ln(~N(t)~~)=0.0104t~\ln(~205e ) }\)
apply the rule ln(a times b)=ln a + ln b

\(\large\color{black}{ \ln(~N(t)~~)=0.0104t~[\ln(~205)+\ln(e )] }\)

ln (e) =1

\(\large\color{black}{ \ln(~N(t)~~)=0.0104t~[\ln(~205)+1] }\)

and in this equation (just like before), you can't solve for 2 unknown variables.
(since it is a single equation with more than 1 unknown).

the "t" or number of years when N(t) doubles,
would depends on the principal value of N(t), saying what N(t) is NOW.

Answer 4

I don't think it has a solution, although using a natural log is certainly the approach when N(t) is given but the "t" is missing.

Sorry that I can't help you.