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Revenue flows into a company at a rate of f(t) = 30001 + 4t, where t is measured in years and f(t) is measured in dollars per year, find the total revenue obtained in the first six years.

Question

Revenue flows into a company at a rate of f(t) = 30001 + 4t, where t is measured in years and f(t) is measured in dollars per year, find the total revenue obtained in the first six years.

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Solution

To find the total revenue obtained in the first six years, we need to integrate the rate function from 0 to 6.

The integral of a function gives the area under the curve, which in this case represents the total revenue over a certain period of time.

The function f(t) = 30001 + 4t represents the rate of revenue flow, so to find the total revenue over the first six years, we integrate this function from 0 to 6.

∫ from 0 to 6 (30001 + 4t) dt

= [30001t + 2t^2] from 0 to 6

= (300016 + 26^2) - (300010 + 20^2)

= 180006 + 72

= 180078

So, the total revenue obtained in the first six years is $180,078.

This problem has been solved

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