An economist has determined that a certain country's gross domestic product (GDP) is approximated by the following function where f(x) is measured in billions of dollars and x is the capital outlay in billions of dollars.f(x) = 620x1/5Use differentials to estimate the change in the country's GDP if the country's capital expenditure changes from $254 billion to $259 billion. (Round your answer to two decimal places.)

Question
Asked Sep 26, 2019
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An economist has determined that a certain country's gross domestic product (GDP) is approximated by the following function where f(x) is measured in billions of dollars and x is the capital outlay in billions of dollars.

f(x) = 620x1/5

Use differentials to estimate the change in the country's GDP if the country's capital expenditure changes from $254 billion to $259 billion. (Round your answer to two decimal places.)

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Expert Answer

Step 1

The change in country GDP can be obtained as follows.

f (x)(620)x3 dx
620
x
5
=124x dx
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f (x)(620)x3 dx 620 x 5 =124x dx

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Step 2

Here x = 254. Th...

dx 259-254
= 5
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dx 259-254 = 5

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Calculus