It will take 12602.68 years.
Solution:
Q(t)=Qe^-kt
Q(t)=0.25Q
0.25Q=Qe^-0.00011t
ln 0.25=-0.00011t
t=(ln 0.25)/-0.00011= 12602.67601
You need to find where the discriminant is less than zero
Remember the discriminant is b^2 - 4ac
a = m
b = -5
c = -2
Set up the inequality like this
(-5)^2 - 4m(-2) < 0
25 + 8m < 0
8m < -25
m < -25/8 < -3.125
So any number less than -3.125 will make this graph have no x-intercepts (or real roots)
Answer:
B.x= -4 and E. x= 10 are the answers
