To solve this problem, we need to understand the concept of exponential decay. The area of undeveloped land decreases at a constant percentage rate annually, which we can model using the formula for exponential decay:
[tex]\[ A = A_0 \times (1 - r)^t \][/tex]
where:
- [tex]\( A_0 \)[/tex] is the initial amount of undeveloped land,
- [tex]\( A \)[/tex] is the remaining amount of undeveloped land after time [tex]\( t \)[/tex],
- [tex]\( r \)[/tex] is the annual decay rate,
- [tex]\( t \)[/tex] is the time in years.
In this scenario:
- The initial amount of undeveloped land [tex]\( A_0 \)[/tex] is 3400 acres.
- The remaining amount of undeveloped land [tex]\( A \)[/tex] is 900 acres.
- The annual decay rate [tex]\( r \)[/tex] is 17.3%, which can be represented as a decimal: [tex]\( 0.173 \)[/tex].
Substituting these values into the formula, we get:
[tex]\[ 900 = 3400 \times (1 - 0.173)^t \][/tex]
Simplifying the expression inside the parentheses:
[tex]\[ 900 = 3400 \times (0.827)^t \][/tex]
This matches equation A:
[tex]\[ 900 = 3400(0.827)^t \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
