Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model the population of the world in the second half of the 20th century. (assume that the growth rate is proportional to the population size.) what is the relative growth rate? use the model to estimate the world population in 1991 and to predict the population in the year 2020.

The populaton in year 1991 will be of 5178.9 million of people

and the population in year 2020 will be of 8524.60 million of people

Step-by-step explanation:

We measure the time t in years and let t=0 in the year 1950.

We measure the population P(t) in millions of people, then P(0)=2560 and P(10) = 3040.

Since we are assuming that dp/dt=kP, this theorem gives the following.

The relative growth rate is about 1.7% per year and the model is

Year 1991 is equal in our formula to 41 and year 2020 is equal to 70. Replacing,

Therefore the populaton in year 1991 will be of 5178.9 million of people and the population in year 2020 will be of 8524.60 million of people

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204