SOLUTION: Suppose that the function : P=15+40*ln(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
Question 581319: Suppose that the function : P=15+40*ln(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 approximate 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 90% provided that law enforcement regarding spammers does not
change.
You can put this solution on YOUR website! Suppose that the function : P=15+40*ln(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 approximate the percentage of spam in the year 2006 to the
nearest tenth of a percent.
x = 2006-2002 = 4
plug that into:
P=15+40*ln(x)
P=15+40*ln(4)
P=15+40*1.3863
P=15+55.4518
P=70.5%
b) Use this model to determine in how many years it will take for the percent of
spam to reach 90% provided that law enforcement regarding spammers does not
change.
Set p to 90 and solve for x:
P=15+40*ln(x)
90=15+40*ln(x)
75=40*ln(x)
1.875 = ln(x)
e^1.875 = x
6.52 years = x
