Answer:
5,6 meaning the answer is 4
Step-by-step explanation:
Answer:
(a) 
(b) 
(c) 80% of the population will have heard the rumor in about 7.4 hrs.
Step-by-step explanation:
We know that a rumor spreads according to the equation

where
is the proportion of the population that knows the rumor at time
, and
and
are positive constants.
(a) To find
you must:
Use this fact,
![\lim _{x\to a}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\lim _{x\to a}f\left(x\right)}{\lim _{x\to a}g\left(x\right)},\:\quad \lim _{x\to a}g\left(x\right)\ne 0](https://tex.z-dn.net/?f=%5Clim%20_%7Bx%5Cto%20a%7D%5Cleft%5B%5Cfrac%7Bf%5Cleft%28x%5Cright%29%7D%7Bg%5Cleft%28x%5Cright%29%7D%5Cright%5D%3D%5Cfrac%7B%5Clim%20_%7Bx%5Cto%20a%7Df%5Cleft%28x%5Cright%29%7D%7B%5Clim%20_%7Bx%5Cto%20a%7Dg%5Cleft%28x%5Cright%29%7D%2C%5C%3A%5Cquad%20%5Clim%20_%7Bx%5Cto%20a%7Dg%5Cleft%28x%5Cright%29%5Cne%200)

Apply this identity, to find 




(b) To find the rate of speed of the rumor you must find the derivative 


(c) To find the time that will take for 80% of the population to hear the rumor, you must substitute a = 10, k = 0.5, and p(t) = 0.8 into
and solve for t


Answer: ![\begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-\frac{2}{3}\quad \mathrm{or}\quad \:x\ge \:0\:\\ \:\mathrm{Decimal:}&\:x\le \:-0.66666\dots \quad \mathrm{or}\quad \:x\ge \:0\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{2}{3}]\cup \:[0,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A-%5Cfrac%7B2%7D%7B3%7D%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%5Cge%20%5C%3A0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BDecimal%3A%7D%26%5C%3Ax%5Cle%20%5C%3A-0.66666%5Cdots%20%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%5Cge%20%5C%3A0%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A-%5Cfrac%7B2%7D%7B3%7D%5D%5Ccup%20%5C%3A%5B0%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
Step-by-step explanation:




N I think because u can tell