Answer:
A.) 1508; 1870
B.) 2083
C.) 3972
Step-by-step explanation:
The general equation for an exponential model is:
A = A0e^rt
A0 represents the initial population
A indicates the final population
r is the growth rate; t denotes time
1)
Considering the years 1750 and 1800
Time interval, t = 1800 - 1750 = 50 years
Starting population = 790
End population = 980
To find the growth rate:
980 = 790e^50r
980/790 = e^50r
Applying the natural logarithm to both sides
In(980/790) = 50r
0.2155196 = 50r
r = 0.2155196/50
r = 0.0043103
Using this growth rate, let's forecast the population for 1900
t = 1900 - 1750 = 150 years
A = 790e^150*0.0043103
A = 790e^0.6465588
A = 1508.0788; approximately 1508 million people
In 1950:
t = 1950 - 1750 = 200
A = 790e^200*0.0043103
A = 790e^0.86206
A = 1870.7467; around 1870 million people
2.)
Exponential model from 1800 to 1850
Initial population in 1800 = 980
Final population in 1850 = 1260
t = 1850 - 1800 = 50
Utilizing the exponential equation, we find the growth rate:
1260 = 980e^50r
1260/980 = e^50r
Taking the natural logarithm of both sides
In(1260/980) = 50r
0.2513144 = 50r
r = 0.2513144/50
r = 0.0050262
Utilizing this model, the anticipated population in 1950:
In 1950:
t = 1950 - 1800 = 150
A = 980e^150*0.0050262
A = 980e^0.7539432
A = 2082.8571; approximately 2083 million people
3.)
For 1900: 1650,
For 1950: 2560
t = 1900 - 1950 = 50
Utilizing the exponential formula, we derive the growth rate:
2560 = 1650e^50r
2560/1650 = e^50r
Logarithm both sides
In(2560/1650) = 50r
0.4392319 = 50r
r = 0.4392319/50
r = 0.0087846
Using this model, the projected population for 2000:
In 2000:
t = 2000 - 1900 = 100
A = 1650e^100*0.0087846
A = 1650e^0.8784639
A = 3971.8787; approximately 3972 million people
