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A function that gives the amount that the plant earns per man-hour t years after it opens is
Given that
A manufacturing plant earned $80 per man-hour of labor when it opened.
Each year, the plant earns an additional 5% per man-hour.
Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.
Amount earned by plant when it is opened = $80 per man-hour
As it is given that each year, the plants earns an additional of 5% per man hour
So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)
Amount earned by plant after two years is given as:
Similarly Amount earned by plant after three years
Hence a function that gives the amount that the plant earns per man-hour t years after it opens is
Answer:
Converges
Sum = 20.8333
Step-by-step explanation:
A geometric series has a general formula of:
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:
Since 0.2 < 1.0, the series converges.
The sum of the series is given by:
The sum is 20.8333.