Respuesta :

apologiabiology

exponential growth is

[tex]y=ab^x[/tex]

we need to find a and b

in form (x,y) we have the points

(0,20), (1,30), (2,45)

subsituting we get

[tex]20=ab^0[/tex], [tex]30=ab^1[/tex] 45=ab^2[/tex]

if we look at the first one

[tex]20=ab^2=a(1)=a[/tex]

so a=20

if we put that into the 2nd one

[tex]30=ab^1=ab=20b[/tex], so b=30/20=3/2


so the formula is [tex]y=20(\frac{3}{2})^x[/tex]

at 11 weeks, x=11

[tex]y=20(\frac{3}{2})^{11}[/tex]

[tex]y=1729.95[/tex]

so about 1730 at the end of the 11th week

Every week, the population grows by half of its current population:

  • by the end of week 0 the population is 20, and it grows by 10, which is half of 20
  • by the end of week 1 the population is 30 and it grows by 15, which is half of 30

So, growing by half means to multiply by 1.5. And as you can see, we start with 20. By the end of week 1 we have multiplied by 1.5 once, by the end of week 2 we have multiplied by 1.5 twice, and so on.

So, at the end of the n-th week, we will have multiplied by 1.5 n times, leading to a population of

[tex] p = 20\cdot 1.5^w [/tex]

where p is the population and w is the number of weeks passed.

So, at the end of the 11-th week, the population will be

[tex] p = 20\cdot 1.5^{11} = 20\cdot 86.4975585938 = 1729.95117188 [/tex]

which is rounded by 1730

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