To determine the equation for the population after [tex]\( t \)[/tex] years, we use the formula for continuous growth which is given by:
[tex]\[ A(t) = P e^{rt} \][/tex]
where:
- [tex]\( A(t) \)[/tex] is the population after [tex]\( t \)[/tex] years,
- [tex]\( P \)[/tex] is the initial population,
- [tex]\( r \)[/tex] is the growth rate, and
- [tex]\( t \)[/tex] is the time in years.
From the problem, we have the following given values:
- The initial population [tex]\( P \)[/tex] is 7,600,000.
- The growth rate [tex]\( r \)[/tex] is 2%, which we convert to a decimal by dividing by 100 to get 0.02.
- The time [tex]\( t \)[/tex] is variable and not specified.
So we can fill in the blanks as follows:
[tex]\[
\begin{array}{l}
A(t) = P e^{rt}, \\
P = 7600000
\end{array}
\][/tex]
[tex]\[ r = 0.02 \][/tex]
[tex]\[ t = ? \][/tex]
Therefore, the completed information is:
- Blank 1: 7600000
- Blank 2: 0.02
- Blank 3: ?
This gives us the equation for the population after [tex]\( t \)[/tex] years:
[tex]\[ A(t) = 7600000 \cdot e^{0.02t} \][/tex]
That's the equation that models the population growth of Honduras assuming the growth rate stays constant.
