Question

#7 – 10 (2 pt each) f(x) = 5200(0.84)* models the number of honey bees in a colony. x is the number of months since the beeswere counted.7) Is the bee population increasing or decreasing?8) At what rate is the population growing or decaying?a. 0.16% b. 16% C. 8.4% d. 84%9) What does the 5200 represent?10) How many bees are in the colony 9 months after first being counted?

Answer 1

At a given function: where, x = the number of months the bees

were counted.

`f(x)=5200(0.84)^x`

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,

`f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^6`
`=\text{ 1,826.7497 }\cong\text{ 1,827}`

At, x = 12,

`f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^(12)`
`=\text{ 641.7336 }\cong642`

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,

`f(x)=5200(0.84)^x\text{ }\rightarrow5200(0.84)^9`
`=\text{ 1082.7219 }\cong1083`

Therefore, the population of bees 9 months after being first counted will be 1083.