SOLUTION: P=12+20In x represents the %of inbound email in the US that is considered spam, where x is the number of years after 2000. Use the model to determine in how many yrs (to 2 decimal

Algebra ->  Probability-and-statistics -> SOLUTION: P=12+20In x represents the %of inbound email in the US that is considered spam, where x is the number of years after 2000. Use the model to determine in how many yrs (to 2 decimal      Log On


   

Question 404254: P=12+20In x represents the %of inbound email in the US that is considered spam, where x is the number of years after 2000. Use the model to determine in how many yrs (to 2 decimals places) it will take the % of spam to reach 90%. Use the model to determine the % of spam in the year 2005. Round to 2 decimal places. Please help these are killing me.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P+=+12+%2B20%2A+ln%28x%29
First, you have to find out what P is in the year 2001
If x is the number of years after 2000, then x+=+1 when
the year = 2001, so
P+=+12+%2B+20%2A+ln%281%29
P+=+12+%2B+20%2A+0
P+=+12 (or, 12%)
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I want to get an idea how fast P increases with x
x+=+2, P+=+12+%2B+20%2A.693 (25.863% in 2002)
x+=+3, P+=+12+%2B+20%2A1.099 (33.972% in 2003)
x+=+4, P+=+12+%2B+20%2A1.386 (39.726% in 2004)
x+=+5, P+=+12+%2B+20%2A1.609 (44.189% in 2005)
OK, x is going to be pretty large.
90+=+12+%2B+20%2Aln%28x%29
20%2Aln%28x%29+=+78
ln%28x%29+=+78%2F20
ln%28x%29+=+3.9
I'll write this as an exponential:
x+=+e%5E3.9
x+=+49.40
So, it takes 49.4 years after 2000, or 2049 + 5 months to reach 90% spam
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Now find P when x+=+5
P+=+12+%2B+20%2Aln%285%29
P+=+12+%2B+20%2A1.609
P+=+12+%2B+32.189
P+=+44.19
The spam is 44.19% in 2005
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I would guess that your problem is:
When they say percent, they don't mean .90, but the actual %, 90