Question

the exponential model $a = 630.9e^{0.027t}$ describes the population, $a$, of a country in millions, $t$ years after 2003. use the model to determine the population of the country in 2003.
the population of the country in 2003 was \\(\square\\) million.

Explanation:

Step1: Identify the value of t

Since we want the population in 2003, and t is the number of years after 2003, so \( t = 0 \).

Step2: Substitute t into the model

The model is \( A = 630.9e^{0.027t} \). Substitute \( t = 0 \):
\( A = 630.9e^{0.027\times0} \)
Since \( e^{0}=1 \), we have \( A = 630.9\times1 = 630.9 \).

Answer:

630.9