Question
he exponential model Upper A equals 144.5 e Superscript 0.004 t 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.
Question content area bottom
Part 1
The population of the country in 2003 was
enter your response here million.
Question content area bottom
Part 1
The population of the country in 2003 was
enter your response here million.
Answers
GPT-4o mini
To determine the population of the country in 2003 using the exponential model \( A = 144.5 e^{0.004t} \), we need to find \( A \) when \( t = 0 \) (which corresponds to the year 2003).
Plugging in \( t = 0 \) into the equation:
\[
A = 144.5 e^{0.004 \cdot 0}
\]
\[
A = 144.5 e^{0}
\]
\[
A = 144.5 \cdot 1
\]
\[
A = 144.5
\]
Therefore, the population of the country in 2003 was **144.5 million**.
Plugging in \( t = 0 \) into the equation:
\[
A = 144.5 e^{0.004 \cdot 0}
\]
\[
A = 144.5 e^{0}
\]
\[
A = 144.5 \cdot 1
\]
\[
A = 144.5
\]
Therefore, the population of the country in 2003 was **144.5 million**.