+524 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.
+128474 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
