Respuesta :
Answer:
Step-by-step explanation:
A) initial psi level = 40
Today, psi level = 38
Amount by which it decreased is 40 - 38 = 2 psi
Percentage by which it reduced is
2/40 × 100 = 5% or 0.05
The exponential model expression is
A = (1 - r)^t
where
A represents the final value after t days
P represents the initial value
r represents the rate of decrease
Therefore, when t = 7, then
A = 40(1 - 0.05)^7
A = 40(0.95)^7
A = 27.9 psi
B) initial cost = 1250
r = 21% = 21/100 = 0.21
The exponential model expression is
A = 1250(1 - 0.21)^t
Where
t represents the number of months
A represents final cost after t months
P represents initial cost
r represents rate
If A = $25, then
25 = 1250(0.79)^t
25/1250 = 0.79^t
0.02 = 0.79^t
Taking log of both sides, it becomes
Log 0.02 = tlog0.79
- 1.699 = - 0.102t
t = - 1.699/-0.102
t = 17 months
C) initial amount = $40000
r = 1.25% = 1.25/100 = 0.0125
The exponential model expression is
A = 40000(1 + 0.0125)^t
When A = $120000, then
120000 = 40000(1.0125)^t
120000/40000 = (1.0125)^t
3 = (1.0125)^t
Taking log of both sides, it becomes
Log 3 = t log 1.0125
0.477 = 0.0054t
t = 0.477/0.0054t
t = 88 years
