The table gives estimates of the world population, in millions, from 1750 to 200

Question

The table gives estimates of the world population, in millions, from 1750 to 2000. (Round your answers to the nearest million.) Year Population 1750 790 1800 980 1850 1260 1900 1650 1950 2560 2000 6080 (a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. 1900 million people 1950 million people (b) Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. million people (c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. million people

Explanation / Answer

So we have given that the table

So the Population formula is P(y) = 790 ek(y-1750)   

If y = 1750 , P = 790 , and If y = 1800 ,P = 980

So we plug this values in the formula above.

So it becomes 980 = 790ek(1800-1750)

980/790 = ek(50)

1.2405 = ek(50)

So we need to take ln on both sides, ln(1.2405) = 50kln(e)

ln(1.2405)/50 = k    (since lne = 1)

So k = 0.004310

So the population formula becomes P(y) = 790e0.00431(y - 1750)

So using this we have to predict the population in the year 1950 and 1900.

So population in 1900, P(1900) = 790e0.00431(1900 - 1750)    = 1507.99

So we get population in 1900 by the formula is 1507.99

If y = 1950, P(1950) = 790e0.00431(1950 - 1750)   = 1870.63

we get population in 1950 by the formula is 1870.63

For the part b , we have to write the formula , Initial year = 1850, So P(y) =1260ek(y-1850)  

for y = 1900, we have P = 1650 , So the formula becomes 1650 = 1260ek(1900-1850)  

1650/1260 = e^(50k)

So we get ln(1.3095) = 50k

So k = 0.005393271

So P(y) = 1260e0.005393271(y-1850)   

So the polpulation in the 1950 by this formula is . P(1950) = 1260e0.005393271(1950-1850)   

P(1950) = 2160.7142

This is the reqiured answer for the part b.

Next, (c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000

So initial year = 1900, so P = 1650 and the formula becomes P(y) = 1650ek(y-1900)

And for y = 1950, we have given P = 2560.

So we get 2560 = 1650ek(1950-1900)

we get k = 0.00878463

So the formula becomes P(y) = 1650e0.00878463(y-1900)

So to find the population in the year y = 2000, we have to plug y = 2000 in the P(y) = 1650e0.00878463(y-1900)

P(y) = 1650e0.00878463(2000-1900)   =3971.8750

This is the predcited population.

Year polulation 1750 790 1800 980 1850 1260 1900 1650 1950 2560 2000 6080

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.