To determine which equation can be used to find the number of years it will take for the undeveloped land in the suburban town to reduce to 900 acres, we can follow these steps:
1. Identify the annual decay rate: The land is decreasing at a rate of [tex]\(17.3\%\)[/tex] annually. This means the remaining percentage each year is:
[tex]\[
100\% - 17.3\% = 82.7\%
\][/tex]
In decimal form, this is:
[tex]\[
0.827
\][/tex]
2. Use the exponential decay formula: The general form of the exponential decay equation is:
[tex]\[
A = P \cdot (1 - r)^t
\][/tex]
In this case:
- [tex]\(A\)[/tex] is the final amount of undeveloped land (900 acres).
- [tex]\(P\)[/tex] is the initial amount of undeveloped land (3,400 acres).
- [tex]\(r\)[/tex] is the decay rate ([tex]\(0.173\)[/tex]).
- Each year, [tex]\(1 - r\)[/tex] is the remaining proportion ([tex]\(0.827\)[/tex]).
- [tex]\(t\)[/tex] is the number of years since 2016.
3. Substitute the values into the equation:
[tex]\[
900 = 3400 \cdot (0.827)^t
\][/tex]
4. Identify the correct form: Comparing this with the given options, the correct equation matches option:
[tex]\[
\boxed{900=3,400(0.827)^t}
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{C. \, 900 = 3,400 (0.827)^t}
\][/tex]
