Answer:
C
Step-by-step explanation:
The number of people who have heard a rumor is modeled by the logistic function:
![\displaystyle f(x)=\frac{260}{1+23e^{-0.06x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D%5Cfrac%7B260%7D%7B1%2B23e%5E%7B-0.06x%7D%7D)
And we want how many days has passed since the rate at which the rumor spread began to decrease.
First, the numerator tells us that the total number of people who will have heard the rumor by the end is 260.
Recall that the point of maximum growth is always half of the maximum capacity.
In this case, that point will be 260/2 = 130.
For a logistic function, the rate of all values to the left of the halfway point is increasing, (i.e. concave up), while the rate of all values to the right is decreasing (i.e. concave down). Therefore, we can solve for x when f(x) = 130:
![\displaystyle 130=\frac{260}{1+23e^{-0.06x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20130%3D%5Cfrac%7B260%7D%7B1%2B23e%5E%7B-0.06x%7D%7D)
Cross-multiply:
![130(1+23e^{-0.06x}})=260](https://tex.z-dn.net/?f=130%281%2B23e%5E%7B-0.06x%7D%7D%29%3D260)
Distribute:
![130+2990e^{-0.06x}=260](https://tex.z-dn.net/?f=130%2B2990e%5E%7B-0.06x%7D%3D260)
Solving for x:
![2990e^{-0.06x}=130](https://tex.z-dn.net/?f=2990e%5E%7B-0.06x%7D%3D130)
Therefore:
![\displaystyle e^{-0.06x}=\frac{130}{2990}=\frac{1}{23}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20e%5E%7B-0.06x%7D%3D%5Cfrac%7B130%7D%7B2990%7D%3D%5Cfrac%7B1%7D%7B23%7D)
Taking the natural log of both sides:
![\displaystyle -0.06x=\ln\Big(\frac{1}{23}\Big)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-0.06x%3D%5Cln%5CBig%28%5Cfrac%7B1%7D%7B23%7D%5CBig%29)
Therefore:
![\displaystyle x=\frac{\ln(1/23)}{-0.06}\approx52.3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B%5Cln%281%2F23%29%7D%7B-0.06%7D%5Capprox52.3)
After about 52.3 days, the rate at which the rumor started spreading will begin to decrease.
Answer:
1/3
Step-by-step explanation:
Answer:
First 1 is 56
2nd one is 112
3rd one is 336
Step-by-step explanation:
Separate the figure into the two shapes: a square and a trapezoid.
The sides of a square are all equal.
Therefore the square has a perimeter of 30 inches (because only three of its sides make up the whole shape)
An isosceles trapezoid has two sides that are equal: the two sides that are opposite each with length 5.
This means that 5 + 5 + 4 = 14.
Add the two perimeters up and you get 44inches.
Answer:40
Step-by-step explanation:
10 devided by .25 = 40