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UkoKoshka [18]
3 years ago
7

A 2000-gallon metal tank to store hazardous materials was bought 15 years ago at cost of $100,000. What will a 5,000-gallon tank

cost today if the power–sizing exponent is 0.57 and the construction cost index for such facilities has increased from 180 to 600 over the last 15 years? Choose the closest value.
Mathematics
1 answer:
harkovskaia [24]3 years ago
8 0

Answer:

The value  is P_o = \$ 561958.9

Step-by-step explanation:

From the question we are told that

  The capacity of the metal  tank is  C =  2000 \  gallon

   The duration usage is  t = 15\ years \ ago

   The cost of 2000-gallon tank 15 years ago is P =  \$100,000

    The capacity of the second tank considered is C_1 = 5,000  

    The power sizing exponent is e = 0.57

     The initial construction cost index is  u_1 = 180

      The new construction after 15 years cost index is  u_2 =600

Equation for the power sizing exponent is mathematically represented as

      \frac{P_n}{P} = [\frac{C_1}{C} ]^{e}

=> Here P_n is the cost of 5,000-gallon tank as at 15 years ago  

So

     P_n  =  [\frac{5000}{2000} ] ^{0.57} * 100000

      P_n  =  \$168587.7

Equation for the cost index exponent is mathematically represented as

      \frac{P_o}{P_n}  =  \frac{u_2}{u_1}

HereP_o is the cost of 5,000-gallon tank today

So

       \frac{P_o}{168587.7}  =  \frac{600}{180}

=>    P_o = \frac{600}{180} * 168587.7

=>      P_o = \$ 561958.9

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