SOLUTION: Suppose that the function P=12+50ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2001. Carry all calcu

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Suppose that the function P=12+50ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2001. Carry all calcu      Log On

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Question 147814: Suppose that the function P=12+50ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2001.
Carry all calculations to six decimals on each intermediate step when necessary.
a) use this model to approximate the percentage of spam in the year 2005. I need to know all steps please.
b) Use this model to determine how many years it will take (to two decimal places) for the percent of spam to reach 90% provided that the law enforcement regarding spammers does not change.
My answer fo first part is P=12+3.91(4) = P=12+15.65 P= 27.65% Is this correct and the second part 90=12+50ln(x), 90=12+3.91(x), 90=15.91x, 15.91years Is this correct? Thanks for help
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Your thinking is correct.
However your calculations are not.
P=12%2B50%2Aln%28x%29
P=12%2B50%2Aln%284%29
P=12%2B50%2A1.386294
I'm not sure where the 3.91 comes in other than from ln(50)=3.91.
That's your mistake.
P=12%2B50%2A1.386294
P=12%2B69.31
P=81.31
And the same for the second part.
The thinking was clear but the calculation had mistakes.
90=12%2B50%2Aln%28x%29
Solve for x.
78=50%2Aln%28x%29 Subtract 12 from both sides.
1.56=ln%28x%29 Divide both side by 50.
x=4.76 Use the inverse of the natural log function (e%5Ex).