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The equation for the situation is
It will take around 9 years for her to have around 5 sheep
Step-by-step explanation:
The exponential decay growth/decay equation is , where
- a is the initial value
- b is the growth/decay factor
- If b > 1, then it is a growth factor
- If 0 < b < 1, then it is a decay factor
Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year
∵ The population is decreased
∴ The equation is decay
∵ The population is two-thirds of the previous year
∴ The decay factor is
∵ She starts with an initial 200 sheep
∴ the initial value is 200
∵ The decay equation is , where y represent the
population in x years
∵ a = 200
∵ b =
∴
The equation for the situation is
∵ The population after x years is around 5 sheep
- Substitute y by 5 to find x
∵
- Divide both sides by 200
∴
- Insert ㏒ for both sides
∴
∴
- Divide both sides by
∴ 9.098 = x
∴ x is around 9 years
It will take around 9 years for her to have around 5 sheep
Learn more:
You can learn more about the equation in brainly.com/question/10666510
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