SOLUTION: After taking his last college Latin course in 2005, Harold knows approximately 20,000 words. Unfortunately, the number of words he remembers decreases according to the model W

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Question 1178977: After taking his last college Latin course in 2005, Harold knows approximately 20,000
words. Unfortunately, the number of words he remembers decreases according to the model
W = 20000(0.904)t where W is the number of words he remembers t years after 2005. How
long before Harold knows only half of the words he learned in college?

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Your exponential formula for decay of the memory is


    W(t) = .


Based on the condition, you write the equation for t as you read your text


    10000 = .


Next, you divide both sides by 20000


    0.5 = .


Now, you take log base 10 of both sides


    log(0.5) = t*log(0.904)


which gives you an expression for time "t"


    t = 


Next you use your calculator and get


    t = 6.868  years.      ANSWER


ANSWER.  6 years and  316 days.

Solved, answered, explained and completed.

----------------

To see many other solved problems on exponential growth/decay,  look into the lessons
    - Population growth problems
    - Radioactive decay problems
    - Carbon dating problems
    - Bacteria growth problems
    - A medication decay in a human's body
    - Problems on appreciated/depreciated values
    - Inflation and Salary problems
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


/////////////


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