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The number of wild flowers growing each year in a meadow is modeled by the function f(x).

 

f(x) = 1000/1+9e^−0.4x

 

Which statements are true about the population of wild flowers?

 

Select each correct answer.

 

  • Initially there were 100 wild flowers growing in the meadow.
  • 42 more wildflowers will grow in the 11th year than in the 10th year.
  • In the 15th year, there will be 1050 wild flowers in the meadow. 
  • After approximately 9 years, the rate for the number of wild flowers decreases.
adore.nuk  Feb 5, 2018
edited by adore.nuk  Feb 5, 2018
 #1
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f(x)  =     1000 /  [ 1 + 9e^(-.4x) ] 

 

Note that......at the start x   = 0....so  e^(-.4(0))  = e^0   =   1

 

So....at the start we have

 

1000 / [  1 + 9(1)]   =    1000 / [ 1 + 9 ]   =  1000 / 10 =  100 flowers

 

So....the first statement is true

 

 

To   answer the next two...look at the calculated results from WolframAlpha :

 

https://www.wolframalpha.com/input/?i=1000+%2F%C2%A0+%5B+1+%2B+9e%5E(-.4x)+%5D,+x+%3D+10,+11

 

10th year  ≈   858         11th year ≈ 900

 

So    900 - 858  =  42    .....the second answer is good, too

 

For the 3rd one......let x  =  15

 

WolframAlpha  calculates   ≈  978....so...the third statement isn't true

 

 

The last one is a little tricky

 

9th year  ≈ 803

10th year ≈  858     increase  =  55

 

10th ≈  858

11th ≈ 900    increase =  42

 

11th ≈ 900

12th ≈ 931   increase  =  31

 

So....the last statement seems to be true, as well

 

 

cool cool cool 

CPhill  Feb 5, 2018

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