Problem

The exponential model $A=55.4 e^{0.002 t}$ 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.
The population of the country in 2003 was $\square$ million.

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The population of the country in 2003 was \(\boxed{55.4}\) million.

Steps

Step 1 :The exponential model $A=55.4 e^{0.002 t}$ 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.

Step 2 :The question asks for the population of the country in 2003. According to the model, t represents the number of years after 2003. Therefore, to find the population in 2003, we need to substitute t = 0 into the model.

Step 3 :Substitute t = 0 into the model: $A = 55.4 e^{0.002 * 0}$

Step 4 :Simplify the equation to find A: $A = 55.4$

Step 5 :Final Answer: The population of the country in 2003 was \(\boxed{55.4}\) million.

link_gpt