Solution for Problem 4.2.2

The population of a country increases according to the model:
P = 100e0.008t where t is time in years with t = 0 corresponding to 2000.
Find the population in 2020. (population given in millions: 100 represent 100,000,000)

Solve

 Step

Find P using P = Poekt       Growth formula
 Identify each part
 
Po= 100
initial amount in millions
t = 20
time in years 2020 - 2000 = 20
k = 0.008
growth constant - given k = 0.008
P = 100e0.008(20)  » 117.4 Growth formula

Interpret Þ There would be about 117.4 million people in the year 2020.

Calculator Help

Most calculators....use ^ or xy for exponent key
HINT: use these key strokes
100×e ^ (0.008 ×20) [enter or =]
Recall e » 2.718281828459045....
 
You will find k in using logarithms in latter sections.