SOLUTION: Suppose that the function P=11+44ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2002. Carry all calculat

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose that the function P=11+44ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2002. Carry all calculat      Log On


   

Question 153055: Suppose that the function P=11+44ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2002. Carry all calculations to six decimals on each intermediate step when necessary.
a. Use this model to determine the percentage of spam in the year 2006 to the nearest tenth of a percent.
b. Use this model to determine in how many years it will take for the percent of spam to reach 85% provided that law enforcement regarding spammers does not change.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the function P(x) = 11 + 44ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2002. Carry all calculations to six decimals on each intermediate step when necessary.
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a. Use this model to determine the percentage of spam in the year 2006 to the nearest tenth of a percent.
P(4) = 11 + 44ln(4) = 71.996952%
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b. Use this model to determine in how many years it will take for the percent of spam to reach 85% provided that law enforcement regarding spammers does not change.
85 = 11 + 44ln(x)
74 = 44ln(x)
lnx = 1.681818
x = e^1.681818 = 5.375320
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Ans: In a little over five years.
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Cheers,
Stan H.