Question

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. Write an equation for the situation? How long will it take for her to have around 5 sheep?

Answer 1

The equation for the situation is $y=200(\frac{2}{3})^{x}$

It will take around 9 years for her to have around 5 sheep

Step-by-step explanation:

The exponential decay growth/decay equation is $y=a(b)^{x}$ , 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 $\frac{2}{3}$

∵ She starts with an initial 200 sheep

∴ the initial value is 200

∵ The decay equation is $y=a(b)^{x}$ , where y represent the

   population in x years

∵ a = 200

∵ b = $\frac{2}{3}$

∴ $y=200(\frac{2}{3})^{x}$

The equation for the situation is $y=200(\frac{2}{3})^{x}$

∵ The population after x years is around 5 sheep

- Substitute y by 5 to find x

∵ $5=200(\frac{2}{3})^{x}$

- Divide both sides by 200

∴ $0.025=(\frac{2}{3})^{x}$

- Insert ㏒ for both sides

∴ $log(0.025)=log(\frac{2}{3})^{x}$

∴ $log(0.025)=xlog(\frac{2}{3})$

- Divide both sides by $log(\frac{2}{3})$

∴ 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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