Determine number of moths until implementation,

Algebra
Tutor: None Selected Time limit: 1 Day

A company estimates that the monthly cost of gradually implementing a new process in its factory can be modeled by the function f(n)=1/4 (2)^0.25n where n is the number of months since implementation began. This cost continues to change up to a maximum monthly cost of m(n)= 200 dollars. Once the monthly cost reaches the maximum of $200, the process is fully implemented. 

a. Write an equation to determine the number of months until full implementation.

May 4th, 2015

Based on the given information, the equation to determine the number of months until full implementation would be

1/4 (2)^0.25n = 200  since full implementation occurs when the monthly cost reaches 200 dollars

May 4th, 2015

Thanks so much that's what I figured :) It's the second part that has me a bit stumped on how to work it exactly.

b. Determine the approximate number of months until the process is fully implemented. Explain how you found your answer.


May 4th, 2015

Ok, then it becomes a matter of solving the equation. This how you do it:

First multiply both sides by 4 to get rid of the 1/4,  that gives you

(2)^0.25n = 800

Now take the log of both sides

log(2)^0.25n = log(800)

Using the rules of logarithm, the exponent is moved to outside of the log

(0.25n)(log2) = log800

0.25n = log800 / log2

0.25n = 9.644

n = 9.644/0.25

n = 38.6 months



May 4th, 2015

Wow that's actually way more simple than I thought! Thanks So Much Mr. A :D

May 4th, 2015

You're very welcome. Glad I could help:)

May 4th, 2015

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