In Example 3.8.1

Question

In Example 3.8.1 we modeled the world population in the second half of the 20th century by the equation P(t) = 2560e0.017185t. Use this equation to estimate the average world population during this time period.

Answer 1

P(t)=2560e^.017185t from t=0 to 50

P(0)=2,560 million in the year 1950

P(50)= 2560e^.017185(50)=6,045.156 million in the year 2000

= about 6 billion

average population is a little < arithmetic average, given upward concavity of the exponential curve

< (6045.156+2560)/2=8605.156/2

< 4,302.578

helps to sketch a graph

find area under the curve = integral of 2560e^.017185t= (2560/.017185)e^.017185t

evaluated from 0 to 50, then divide by base=50 = average height

= [(2560/.017185)e^.017185(50) -2560/.017185]/50

= 4,056.04 million = average population from 1950 to 2000