We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Help please?

0
571
1
+594

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.
Feb 5, 2018
edited by adore.nuk  Feb 5, 2018

### 1+0 Answers

#1
+100516
+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

Feb 5, 2018