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
Algebra ->
Exponential-and-logarithmic-functions
-> 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
Log On
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(52802) (Show Source):
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. ANSWERANSWER. 6 years and 316 days.
