Answer:
The value is [tex]P_o = \$ 561958.9 [/tex]
Step-by-step explanation:
From the question we are told that
The capacity of the metal tank is [tex]C = 2000 \ gallon[/tex]
The duration usage is [tex]t = 15\ years \ ago[/tex]
The cost of 2000-gallon tank 15 years ago is [tex]P = \$100,000[/tex]
The capacity of the second tank considered is [tex]C_1 = 5,000[/tex]
The power sizing exponent is [tex]e = 0.57[/tex]
The initial construction cost index is [tex]u_1 = 180[/tex]
The new construction after 15 years cost index is [tex]u_2 =600[/tex]
Equation for the power sizing exponent is mathematically represented as
[tex]\frac{P_n}{P} = [\frac{C_1}{C} ]^{e}[/tex]
=> Here [tex]P_n[/tex] is the cost of 5,000-gallon tank as at 15 years ago
So
[tex]P_n = [\frac{5000}{2000} ] ^{0.57} * 100000[/tex]
[tex]P_n = \$168587.7[/tex]
Equation for the cost index exponent is mathematically represented as
[tex]\frac{P_o}{P_n} = \frac{u_2}{u_1}[/tex]
Here[tex]P_o[/tex] is the cost of 5,000-gallon tank today
So
[tex]\frac{P_o}{168587.7} = \frac{600}{180}[/tex]
=> [tex]P_o = \frac{600}{180} * 168587.7[/tex]
=> [tex]P_o = \$ 561958.9 [/tex]
