At a given function: where, x = the number of months the bees
were counted.
[tex]f(x)=5200(0.84)^x[/tex]
7.) Let's determine if the bee is increasing or decreasing by determining the population after x = 6 months and x = 12 months.
At, x = 6,
[tex]f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^6[/tex][tex]=\text{ 1,826.7497 }\cong\text{ 1,827}[/tex]
At, x = 12,
[tex]f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^{12}[/tex][tex]=\text{ 641.7336 }\cong642[/tex]
Observing the output at x = 6 and x = 12, it appears that the bee population is Decreasing.
8.) The rate of decaying is at 84%.
9.) 5200 represents the initial population or the first count of the number of bees.
10.) At x = 9,
[tex]f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^9[/tex][tex]=\text{ 1082.7219 }\cong1083[/tex]
Therefore, the population of bees 9 months after being first counted will be 1083.
