The table gives estimates of the world population, in millions, from 1750 to 2000. year population year population 1750 790 1900 1650 1800 980 1950 2560 1850 1260 2000 6080 (a) use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. compare with the actual figures

The poopulation exponential model is given by



Where, P(t) is the population after year t; Po is the initial population, t is the number of years from the starting year; k is the groth constant.

Given that the population in 1750 is 790 and the population in 1800 is 970, we obtain the population exponential equation as follows:



Thus, the exponential equation using the 1750 and the 1800 population values is

The population of 1900 using the 1750 and the 1800 population values is given by



The population of 1950 using the 1750 and the 1800 population values is given by



From the table, it can be seen that the actual figure is greater than the exponential model values.

The exponential function is given by y = 790(1.004)ˣ

Exponential function

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population in millions after x years above 1750.

At 1750 (x = 0):

790 = ab⁰

a = 790

At 1800 (x = 50)

980 = 790(b)⁵⁰

b = 1.004

The exponential function is given by y = 790(1.004)ˣ

At 1900 (x = 100):

y = 790(1.004)¹⁰⁰ = 1215

At 1950 (x = 150):

y = 790(1.004)¹⁵⁰ = 1438

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70°

Step-by-step explanation:

angle AMX and angle YMB are vertical angles.

Vertical angles are congruent.