9514 1404 393
Answer:
- annually: 9.01 years
- monthly: 8.69 years
- daily: 8.67 years
- continuously: 8.66 years
Step-by-step explanation:
For interest compounded in discrete intervals, the formula is ...
A = P(1 +r/n)^(nt)
We want to find t for P=1 and A=2, so we have ...
2 = (1 +r/n)^(nt)
ln(2) = nt·ln(1+r/n)
t = ln(2)/(n·ln(1+r/n))
A table of values for r=0.08 is attached.
__
For continuous compounding, the formula is ...
A = Pe^(rt)
t = ln(A/P)/r = ln(2)/0.08 ≈ 8.66434 . . . . years
__
- annually: 9.01 years
- monthly: 8.69 years
- daily: 8.67 years
- continuously: 8.66 years
Answer:
![(2,8]](https://tex.z-dn.net/?f=%282%2C8%5D)
Step-by-step explanation:
Given
The attached piece wise function
Required
The domain
To do this, we simply consider the inequalities that bound the values of x.
The inequalities are:
and 
Combine the first two inequalities:
and 
For the inequality to be true, we must have:

In interval notation, the inequality is:
![(2,8]](https://tex.z-dn.net/?f=%282%2C8%5D)
It is two units shifted downwards. you can see it by substituting x=0 for both equations