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The exponential model [tex]$A = 815.4 e^{0.002 t}$[/tex] describes the population, [tex]A[/tex], of a country in millions, [tex]t[/tex] years after 2003. Use the model to determine the population of the country in 2003.

The population of the country in 2003 was [tex]\square[/tex] million.



Answer :

GinnyAnswer
To determine the population of the country in 2003 using the exponential model [tex]\( A = 815.4 e^{0.002t} \)[/tex]:

1. Identify the key parameters in the model:
- [tex]\( A \)[/tex] is the population of the country in millions.
- [tex]\( t \)[/tex] is the number of years after 2003.
- The base population at [tex]\( t = 0 \)[/tex] is 815.4 million.
- The growth rate is 0.002 per year.

2. To find the population in 2003, set [tex]\( t \)[/tex] to 0 since 2003 is the base year from which time is measured.

3. Substitute [tex]\( t = 0 \)[/tex] into the exponential model:
[tex]\[ A = 815.4 e^{0.002 \times 0} \][/tex]

4. Simplify the exponent:
[tex]\[ A = 815.4 e^0 \][/tex]

5. Recall that [tex]\( e^0 = 1 \)[/tex]:
[tex]\[ A = 815.4 \times 1 \][/tex]

6. Therefore:
[tex]\[ A = 815.4 \][/tex]

The population of the country in 2003 was [tex]\( 815.4 \)[/tex] million.

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