Answer:
v(h) represents the volume of the water (ft³) in the pool at h hours
h is the number of hours
When h increased v(h) decreased
Step-by-step explanation:
- A swimming pool has about 603 cubic feet of water
∴ The volume of the water in the pool initially is 603 feet³
- The pool liner has a small hole and is leaking at a rate of 15 cubic
feet each hour
∴ The rate of decreasing of the volume of the water in the pool is
15 feet³ per hour
- The volume of the the water v at a time h hour can represented by
a linear function v(h)
∴ v(h) = -15 h + 603 , where v(h) is the volume of the water in the
pool in cubic feet at h hour
- Let us put an example to understand the relation between v(h)
and h
- Assume that h = 0
∵ h = 0
∴ v(0) = -15(0) + 603
∴ v(0) = 603 ft³ ⇒ The volume of the water at the beginning
- Assume that h = 2 hours, that means we need to know the volume
of the water after two hours
∵ h = 2 hours
∴ v(2) = -15(2) + 603
∴ v(2) = -30 + 603 = 573 ft³
∵ h increased from 0 to 2
∴ v(t) decreased from 603 ft³ to 573 ft³
∴ The volume decreased when the number of hours increased
* v(h) represents the volume of the water (ft³) in the pool at h hours
* h is the number of hours
* When h increased v(h) decreased
converges if 
is monotonic and 
as 
. Here 
.
. Then 
, which is positive for all 
, so 
is monotonically increasing for 
must be a monotonically decreasing sequence over the same interval, and so must 
.