Answer:
The value is ![P_o = \$ 561958.9](https://tex.z-dn.net/?f=P_o%20%3D%20%5C%24%20561958.9%20)
Step-by-step explanation:
From the question we are told that
The capacity of the metal tank is ![C = 2000 \ gallon](https://tex.z-dn.net/?f=C%20%3D%20%202000%20%5C%20%20gallon)
The duration usage is ![t = 15\ years \ ago](https://tex.z-dn.net/?f=t%20%3D%2015%5C%20years%20%5C%20ago)
The cost of 2000-gallon tank 15 years ago is ![P = \$100,000](https://tex.z-dn.net/?f=P%20%3D%20%20%5C%24100%2C000)
The capacity of the second tank considered is
The power sizing exponent is ![e = 0.57](https://tex.z-dn.net/?f=e%20%3D%200.57)
The initial construction cost index is ![u_1 = 180](https://tex.z-dn.net/?f=u_1%20%3D%20180)
The new construction after 15 years cost index is ![u_2 =600](https://tex.z-dn.net/?f=u_2%20%3D600)
Equation for the power sizing exponent is mathematically represented as
![\frac{P_n}{P} = [\frac{C_1}{C} ]^{e}](https://tex.z-dn.net/?f=%5Cfrac%7BP_n%7D%7BP%7D%20%3D%20%5B%5Cfrac%7BC_1%7D%7BC%7D%20%5D%5E%7Be%7D)
=> Here
is the cost of 5,000-gallon tank as at 15 years ago
So
![P_n = [\frac{5000}{2000} ] ^{0.57} * 100000](https://tex.z-dn.net/?f=P_n%20%20%3D%20%20%5B%5Cfrac%7B5000%7D%7B2000%7D%20%5D%20%5E%7B0.57%7D%20%2A%20100000)
![P_n = \$168587.7](https://tex.z-dn.net/?f=P_n%20%20%3D%20%20%5C%24168587.7)
Equation for the cost index exponent is mathematically represented as
![\frac{P_o}{P_n} = \frac{u_2}{u_1}](https://tex.z-dn.net/?f=%5Cfrac%7BP_o%7D%7BP_n%7D%20%20%3D%20%20%5Cfrac%7Bu_2%7D%7Bu_1%7D)
Here
is the cost of 5,000-gallon tank today
So
![\frac{P_o}{168587.7} = \frac{600}{180}](https://tex.z-dn.net/?f=%5Cfrac%7BP_o%7D%7B168587.7%7D%20%20%3D%20%20%5Cfrac%7B600%7D%7B180%7D)
=> ![P_o = \frac{600}{180} * 168587.7](https://tex.z-dn.net/?f=P_o%20%3D%20%5Cfrac%7B600%7D%7B180%7D%20%2A%20168587.7)
=> ![P_o = \$ 561958.9](https://tex.z-dn.net/?f=P_o%20%3D%20%5C%24%20561958.9%20)