For this problem, we have the final population #P#, the starting population #A#, and the time passed #t#.
We still need to determine the value of the growth factor #k#.
This can be done using the information for the years #1994# and #2002#.
In this case, #A# will be #195# million (the population in #1994#), #P# will be #199# million (the population in #2002#), and #t# will be #8# years (the number of years between #1994# and #2002#):
#Rightarrow P = A e^(k t)#
#Rightarrow 199 = 195 e^(k times 8)#
#Rightarrow frac(199)(195) = e^(8 k)#
Applying #ln# to both sides of the equation:
#Rightarrow ln(frac(199)(195)) = ln(e^( 8k))#
Using the laws of logarithms:
#Rightarrow 8 k ln(e) = ln(199) - ln(195)#
#Rightarrow 8 k = ln(199) - ln(195)#
#Rightarrow k = frac(ln(199) - ln(195))(8)#
#therefore k = 0.00253815825#
Now, let's use this information to determine #P# in #2016#.
#A# will still be #195# million, but #t# will be #22# years.
#Rightarrow P = 195 e^(0.00253815825 times 22)#
#Rightarrow P = 195 e^(0.0558394815)#
#Rightarrow P = 195 times 1.057427933#
#therefore P = 206.19844694#
Therefore, the population in #2016# will be around #207# million.
