Question

Note: When solving for k, round to four decimals places **

A country population in 1994 was 195 million. In 2002 it was 199 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest million.

P=Ae^kt

Answer 1

First we find k by using the two values given:
P=Ae^(kt), 8 years between-->t=8
199 = 195•e^(8k)
Log 199 = Log [195•e^(8k)]
Log 199 = Log 195 + 8k
8k = Log 199 - Log 195
k = 0.00882/8 = .0011
Next, we plug the new data in using this k:
14 years between 2002-2016-->t=14
P = Ae^my
P = 199mi.•e^(14•.0011)
P = 199mi.•e^(.0154)
P = 199mi. • 1.0155 = 202,088,000