Please just don't get it....Suppose that the function?

Question

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.

Answer:

b) Use this model to approximate the year that the percent of spam will reach 90% provided that law enforcement regarding spammers does not change?

Answer:

Answer 1

a) The year 2005 is 4 years after 2001, so we need to use x = 4 to solve for P.

P = 12 + 50 * (ln 4)
= 12 + 50 * (1.386294)
= 12 + (69.314718) = 81.314718%

So, in the year 2005, 81.314718% of incoming e-mails will be spam, according to the model.

b) This time, we're given what the percentage P is (90%), and we're asked to find x.

So, 90 = 12 + 50 * (ln x)
78 = 50 * (ln x)
1.56 = ln x
x = e ^ (1.56) = 4.758821

So, in 4.758821 years after 2001, 90% of incoming e-mails will be spam, according to the model.

Answer 2

P(2005) = 12+50ln4 =81.3147181 5%
90 = 12+50lnx so ln x= 78/50 and x= 4.7588212 rounding 5
so it would be in 2006

Answer 3

a. P= 12 + 50ln (4)






b. Set P=90 like this.

90=12+50ln (x) then solve for x

Step 1.
50ln(x) = 78
ln (x) = (78/50)

Got it from there?

Answer 4

a. P = 12 + 50ln4 = 81.314718

b. 90 = 12 + 50ln(x-2001)
ln(x-2001) = (90-12)/50 = 1.56
x - 2001 = exp(1.56) = 4.758821
x = 2004.752882