Response:
The goat population will reach 1000 in a time span of 12.4 years
Detailed explanation:
After t years, the population of goats is described by
where 
indicates the initial count of goats and b is the growth rate per capita.
Based on the problem,
- b = 0.5
- N = 1000
A(w) = -w² + 100w
Step-by-step explanation: Initially, we need to express the length (l) of the rectangular area in terms of the width (w). Given that the total perimeter of the rectangle is 200 feet implies that 2(w + l) = 200, leading to l = 100 - w. Hence, the area A can be given as width multiplied by length: A = w * l = w * (100 - w) = -w² + 100w. Consequently, A(w) = -w² + 100w.
