(a) growing: (i),(ii),(iv) shrinking: (iii),(v),(vi) (b) fastest growth: (iv) @ 18.5% per year (c) fastest shrinking: (v) @ 22% per year (d) largest initial population: (iii) smallest initial population: (ii)
Work Step by Step
(a) (i),(ii),(iv) are growing in size because their growth factor is greater than 1, which means that it's increasing. (iii),(v),(vi) are shrinking in size because their growth factor is less than 1, which means that it's decreasing. (b) (iv) is growing the fastest because it has the highest rate and growth factor, of 18.5% (1.185 - 1 = .185 x 100% = 18.5%) (c) (v) is shrinking the fastest because it has the lowest rate, of 22% ( 1 - 0.78 = 0.22 x 100% = 22%) (d) initial value is given by ''a'' in the exponential equation. Therefore, the largest ''a'' is (iii), 2500, so it has the largest initial population. However, (ii) has the smallest ''a'', 600, which means that is has the smallest initial population.