Original Investment $t$ Is the Time in Years $r$ Is the Annual Interest Rate Compounded Continuously, And

question 29

Multiple Choice

$\text { Suppose the capitalized cost } C \text { is given by } C = C _ { 0 } + \int _ { 0 } ^ { n } c ( t ) e ^ { - n } d t \text {, where } C _ { 0 } \text { is the }$ original investment, $t$ is the time in years, $r$ is the annual interest rate compounded continuously, and $c ( t )$ is the annual cost of maintenance. Find the capitalized cost $C$ of an asset forever if
$C _ { 0 } = 625,000 , c ( t ) = 23,500 ( 1 + 0.07 t )$ , and $r = 0.05$ . Round your answer to the nearest dollar.

• A) 681,400
• B) \(1,753,400\)
• C) \(1,799,511\)
• D) 681,420
• E) \(1,753,000\)

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