The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
It will take around 9 years for her to have around 5 sheep
Step-by-step explanation:
The exponential decay growth/decay equation is [tex]y=a(b)^{x}[/tex] , where
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 [tex]\frac{2}{3}[/tex]
∵ She starts with an initial 200 sheep
∴ the initial value is 200
∵ The decay equation is [tex]y=a(b)^{x}[/tex] , where y represent the
population in x years
∵ a = 200
∵ b = [tex]\frac{2}{3}[/tex]
∴ [tex]y=200(\frac{2}{3})^{x}[/tex]
The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
∵ The population after x years is around 5 sheep
- Substitute y by 5 to find x
∵ [tex]5=200(\frac{2}{3})^{x}[/tex]
- Divide both sides by 200
∴ [tex]0.025=(\frac{2}{3})^{x}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(0.025)=log(\frac{2}{3})^{x}[/tex]
∴ [tex]log(0.025)=xlog(\frac{2}{3})[/tex]
- Divide both sides by [tex]log(\frac{2}{3})[/tex]
∴ 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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