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Olin [163]
3 years ago
14

Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notic

es 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?
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
8 0

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

#LearnwithBrainly

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jonny [76]

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<h2>Procedure - Surface area of a tunnel for a toy train</h2>

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<h3>Determination of the surface area of the tunnel based on information of the diagram</h3>

We calculate the surface area as following:

A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)

A = 614.197\pi\,cm^{2}

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To learn more on surface areas, we kindly invite to check this verified question: brainly.com/question/2835293

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zubka84 [21]

Answer:

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Step-by-step explanation:

given data

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time = 5 year  = 10 half yearly

rate = 4.04 %

to find out

value of final buyout

solution

we know here loan amount will be 25077 - 3560 = $21517

and we find present value first by formula that is

present value = \frac{amount(1+r)^t - 1}{r (1+r)^t}

put here t = 10 and r = \frac{4.04}{200}

so

present value = \frac{2016(1+\frac{4.04}{200})^10 - 1}{r (1+\frac{4.04}{200})^10}

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so

loan unpaid amount is here

loan unpaid amount = 21517 - 18089.96

loan unpaid amount = $3427.04

so

now we calculate value of buyout

that is express as

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amount = 4185.74

so value of buyout is $4185.74

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Step one:'

given data

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DanielleElmas [232]

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Step-by-step explanation:

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