Problem 1 a k b Based on your equation above what is the ann

Problem #1

a=__________

k=__________

(b) Based on your equation above, what is the annual percentage growth rate of N? (Enter your answer in exact form, or a numerical approximation that is accurate to 0.01 %.

By_________%

(c) What is the doubling time of N?  ________ years

Problem #2

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.
log(5(x^(2)-y^(2)))=________________

Problem #3

Using laws of logarithms, write the expression below as a single logarithm.

Solution

1. a) in 1998 no.of users ---- 37.1 million

in 2005 no. of users----- 352.8 million

N(t) = ae^(kt)

a = 37.1

Lets calculate b:

t = 7yrs; 352.8 = 37.1e^(7k)

9.5 = e^(7k)

Taking natural log of both sides:

ln9.5 = 7k

k =0.322

b) Annual percentage growth rate = {(352.8 -37.1)/37.1}*100/ 7 = 121.56%

c) Doubling time:

2*37.1 = 37.1e^(0.322t)

taking natural log of both sides:

t = 2.15 years

2)   log(5(x^(2)-y^(2)))

Using the log property: log(A*B/C) = logA +logB -logC

LogA^x = x*logA

So,log(5(x^(2)-y^(2))) = log5 + log(x^2 -y^2)

= log5 +log(x+y)(x-y) = log5 + log(x+y) + log(x -y)