A manufacturer of the sports goods produced 10000 hockey kit in 50th year and 18000 in 80th year asumeing that the product uniformly by a fixed number find the production in 12th year and in which year the production will 28000 kits
Answers
Answer:
Since, the product uniformly by a fixed number,
Thus, the function that shows the given situation will be linear,
Let the function that shows the production after x years,
f(x) = Ax + B
where A and B are any numbers,
Since, for x = 50, f(x) = 10000
⇒ 10000 = 50 A + B ---------(1)
And, for x = 80, f(x) = 18000
⇒ 18000 = 80 A + B --------(2)
By solving equation (1) and (2),
We get,
A = 800/3 and B = -10000/3
Hence, the function that shows the given situation,
f(x) = 800/3 x - 10000/3
For x = 12
f(12) = 800/3 × 12 - 10000/3 = negative number
Hence, there is no manufacturing in 12th year,
Also, for f(x) = 28000
28000=800/3 x - 10000/3
84000 = 800x - 10000
94000 = 800x
117.5 = x
Hence, approximate after 118 year the production will be 28000.
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