Machine component question? life-expectancy is f(x) = 13 + 12.5 ln(x), for month x

[poseidn]

Question 3: The life expectancy in months, at manufacture, of a machine component manufactured in month x is approximated by the following function:

. . . . .\(\displaystyle f(x)\, =\, 13.0 + 12.5\, \ln(x)\)

...where "x = 10" corresponds to components made in January 2015, "x = 11" to those made in February 2015, and so on.

The formula represents a situation where, due to improved manufacturing processes and better quality control, the durability of components is improving and components made more recently have a longer life expectancy.

(a) Find the life expectancy, to the nearest number of whole months, of machines manufactured in:

. .(i) June 2016, and

. .(ii) September 2015

(b) If this model remains valid, at what whole-month number will the life expectancy of the component be 5 years?

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How do i do this?

Thanks

 

[Deleted member 4993]

Question 3: The life expectancy in months, at manufacture, of a machine component manufactured in month x is approximated by the following function:

. . . . .\(\displaystyle f(x)\, =\, 13.0 + 12.5\, \ln(x)\)

...where "x = 10" corresponds to components made in January 2015, "x = 11" to those made in February 2015, and so on.

The formula represents a situation where, due to improved manufacturing processes and better quality control, the durability of components is improving and components made more recently have a longer life expectancy.

(a) Find the life expectancy, to the nearest number of whole months, of machines manufactured in:

. .(i) June 2016, and

. .(ii) September 2015

(b) If this model remains valid, at what whole-month number will the life expectancy of the component be 5 years?

---

How do i do this?

Thanks

What are your thoughts?

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[stapel]

Question 3: The life expectancy in months, at manufacture, of a machine component manufactured in month x is approximated by the following function:

. . . . .\(\displaystyle f(x)\, =\, 13.0 + 12.5\, \ln(x)\)

...where "x = 10" corresponds to components made in January 2015, "x = 11" to those made in February 2015, and so on.

The formula represents a situation where, due to improved manufacturing processes and better quality control, the durability of components is improving and components made more recently have a longer life expectancy.

(a) Find the life expectancy, to the nearest number of whole months, of machines manufactured in:

. .(i) June 2016, and

. .(ii) September 2015

(b) If this model remains valid, at what whole-month number will the life expectancy of the component be 5 years?

---

How do i do this?

Where are you stuck in the process?

You've been given a function that gives life-expectancy f in terms of manufacture date x (in months).

(a) You are asked for the life-expectancy. Which variable stands for this? So for which variable are you trying to find the value? So for which variable must they have provided you with values?

(i) You are given that "x" is in months, with "January 2015" being when x = 10. How many months after January 2015 is June 2016? So what number should you be adding to "10"? So what is the value of the input variable? So what is the value of the other variable?

(ii) Use the exact same process here, except that you'll be subtracting rather than adding.

(b) You are asked to find the whole-month number. Which variable stands for this? So for which variable are you trying to find the value? So for which variable must they have provided you with a value?

You are given that the life-expectancy is 5 years. You are given that the function for life-expectancy measures this value in months. So what must be the value for the life-expectancy?

When you plug the known value into the given formula and solve the resulting linear equation, what do you get?

If you get stuck, please reply showing all your work in answering the above questions. Thank you!