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

#1**+2 **

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

CPhill Feb 5, 2018