Respuesta :

Roxanne194

Answer:

okay so first we are given that P(2016) = 500 and

P(2017) = 672

put in the equation Pn+1 = k[Pn + 60]

put Pn = P(2016) = 500 {n = 2016 here. }

and P(n+1) = 672

now , 672 = k [ 500 + 60 ]

672 = 560k

k = 672 ÷560 = 1.2

now, using k = 1.2

put n = 2017 in equation we get,

P(2018) = 1.2[ P(2017) + 60 ]

P(2018) = 1.2 [ 672 + 60 ]

P(2018) = 878

now, similarly put n = 2018

P(2019) = k [P(2018) + 60 ]

P(2019) = 1.2 [ 878 + 60 ]

P(2019) = 1125 (approx.)

Sorry for bad graphic style.. I am not very advanced at this.

semsee45

Answer:

1126

Step-by-step explanation:

Given formula:

[tex]P_{n+1}=k(P_n+60)[/tex]

Given information:

  • [tex]\textsf{Let }P_1 = \textsf{Population on March 1st 2016} =500[/tex]
  • [tex]\textsf{Let }P_2 = \textsf{Population on March 1st 2017} =672[/tex]

Substitute these values into the formula and solve for k:

[tex]\begin{aligned}P_{n+1} & = k(P_n+60)\\\implies P_2 & = k(P_1+60)\\672 & = k(500+60)\\672 & = 560k\\k & = \dfrac{672}{560}\\k & = 1.2\end{aligned}[/tex]

Substitute the found value of k into the formula:

[tex]P_{n+1}=1.2(P_n+60)[/tex]

If:

  • P₁ = Population on March 1st 2016
  • P₂ = Population on March 1st 2017

Then:

  •  P₃ = Population on March 1st 2018
  • P₄ = Population on March 1st 2019

Use the formula and the value of P₂ to find P₃ and P₄.

[tex]\begin{aligned}P_{3} & =1.2(P_2+60)\\& = 1.2(672+60)\\& = 878.4\end{aligned}[/tex]

[tex]\begin{aligned}P_{4} & =1.2(P_3+60)\\& = 1.2(878.4+60)\\& = 1126.08\end{aligned}[/tex]

Therefore, the prediction for the population on 1st March 2019 is 1126 tadpoles (nearest whole number).

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