To solve the problem, we need to model the growth of the purple loosestrife plant over time, using the provided values. Let's define the variables and set up the inequality:
1. Initial Area (A): This is the initial area that the purple loosestrife currently covers, which is 500 acres.
2. Growth Rate (b): Each year, the area covered by the plant grows by 20%. This can be represented as a multiplier of the current area: [tex]\( 1 + 0.20 = 1.2 \)[/tex].
3. Target Area (c): The target area we are interested in is 850 acres; we want to find out when the plant will cover more than this area.
The inequality representing the scenario where the purple loosestrife will cover more than 850 acres in [tex]\( t \)[/tex] years can be written using these values:
[tex]\[ 500 \cdot (1.2)^t > 850 \][/tex]
Thus, the values for [tex]\( A \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are:
[tex]\[ A = 500 \][/tex]
[tex]\[ b = 1.2 \][/tex]
[tex]\[ c = 850 \][/tex]
So, the inequality that models the number of years [tex]\( t \)[/tex] for which purple loosestrife will cover more than 850 acres of the wetland is:
[tex]\[ 500 \cdot (1.2)^t > 850 \][/tex]
