Question 301235
In 2005, consumers received, on average, 3253 spam messages.
 The volume of spam messages per consumer is decreasing exponentially with an
 exponential decay rate of 13.7% per year.
:
a) Find the exponential decay function that can be used to predict the average
 number of spam messages, t years after 2005.
The equation: 
S = 3253(1-.137)^t
S = 3253(.863)^t
:
b) Predict the number of spam messages received per consumer in 2010.
t=5
S = 3253(.863)^5
S = 1557 spam msg in 2010

c) In what year, theoretically, will the average consumer receive 100 spam messages?
S = 100: 
3253(.863)^t = 100
(.863)^t = {{{100/3252}}}
.863^t = .03074
t*log(.863) = log(.03074
t = {{{log(.03074)/log(.863)}}}
t = 23.6 ~ 24 yrs
:
2005 + 24 = 2029 yr when spam msg down to 100
:
:
Check solution in a calc: enter 3253(.863)^23.6 = 100.5, close enough