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.
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.
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