Lesson More problems on logarithmic equations

This Lesson (More problems on logarithmic equations) was created by by ikleyn(53339)

: View Source, Show
About ikleyn:

More problems on logarithmic equations

Problem 1

An equipment costing $250,000 has an estimated life of 15 years with a book value of $30,000
at the end of the period. Compute its book value after 10 years using exponentially declining depreciation model.

Solution

We use exponential function for the declining current cost of the equipment

    C(t) = ,  (1)     


where  't'  is time in years.


Since the initial cost is $250,000,  we have  a = 250000  in this formula.

Since the book value is $30,000  in 15 years, we have this equation


    30000 = ,


which gives  

     = ,

     = ,


Take logarithm of both sides

    log(3/25) = 15*log(b)    

    log(b) =  = -0.061387917.


Hence,  b =  = 0.86818461.


Now we are in position to answer the problem's question using formula (1)

    C(10) =  = 60822.01984


ANSWER.  In 10 years, the appreciate value of the equipment will be about $60,822.

My other lessons in this site on logarithms, logarithmic equations and relevant word problems, section 2, are
- Solving logarithmic equation of the level even higher than upper
- OVERVIEW of lessons on logarithms, logarithmic equations and relevant word problems, section 2

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

This lesson has been accessed 95 times.