Mathematics, 31.08.2019 05:30 kbenitez90

If the population of a country is reported in the year 1990 as 471.56 million and in the year 2000 as 492.53 million, when will the population reach 550 million (round your answer to the nearest whole number)? 15 years 35 years o 25 years 5 years

Answers: 2

Show answers

Answers

Answer from: marianasanin2007

35 years

Step-by-step explanation:

It will make this problem a whole lot easier if we call the year 1990 our initial year, or year 0; that means that the year 2000 is year 10. The coordinates then that result from that change are (0, 471.56) and (10, 492.53). Population growth is always exponential, and the formula for that, in terms of x and y, where x is the year and y is the population in millions, is

y=a(b)^x

a is the initial population at year 0 and b is the growth rate. If the growth rate is a decimal (less than 1) what we have is decay as opposed to growth. In order to determine when (x) the population (y) is 492.53, we have to find the model by solving for a and b using the coordinates. Once we find this model, we will use it to solve for x by filling in the y of 550 million. So here we go.

Using the first coordinate, we know that at year 0 the population is 471.56. So that is our initial population, a in our formula. Using that value of a and plugging it in to the formula with the other coordinate gives us

$492.53=471.56(b)^{10}$

Now we have to solve for b. Begin by dividing both sides by 471.56 to get

$1.044469421=b^{10}$

"Undo" that 10th power by taking the 10th root of both sides which gives you that b = 1.004360381

Now we have our model:

y=471.56(1.00436)^x

We will plug in a y value of 550 and solve for x using natural logs.

550=471.56(1.004360381)^x

Begin by dividing both sides by 471.56 to get

1.166341505=(1.004360381)^x

In order to solve for x we have to pull it down from the position in which it is currently sitting, which is an exponent. Taking the natural log of both sides will solve that problem for us:

ln(1.166341505)=ln(1.004360381)^x

The power rule for natural logs tells us we can pull the exponent down in front giving us:

ln(1.166341505)=x*ln(1.004360381)

Now we will divide both sides by ln(1.004360381) to isolate the x. Doing that and at the same time finding those values on our calculator gives us:

$\frac{.153871931}{.0043505227}=x$ so

x = 35

Answer from: Quest

the graph on the bottom right

Answer from: Quest

theres no picture: /

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Complete the statements about the system of linear equation respresented by the tables the equation respented the left table is

Answers: 2

Answer

Mathematics, 21.06.2019 16:10

Abox contains 1 plain pencil and 4 pens. a second box contains 5 color pencils and 5 crayons. one item from each box is chosen at random. what is the probability that a plain pencil from the first box and a color pencil from the second box are selected? write your answer as a fraction in simplest form.

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

What is the arc length when θ =pi over 3 and the radius is 5 cm? (5 points) 5 pi over 3 cm 10 pi over 3 cm 16 pi over 3 cm pi over 3 cm

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Asailor is looking at a kite. if he is looking at the kite at an angle of elevation of 36and the distance from the boat to the point where the kite is directly overhead is 40 feet, how high is the kite?

Answers: 3

Answer

You know the right answer?

If the population of a country is reported in the year 1990 as 471.56 million and in the year 2000 a...

Questions