Respuesta :
Answer:
2054
Step-by-step explanation:
The equation for the growth of people = 308.7(1097)^x
The equation for the growth of vehicles = 246(1155)^x
If the number of both are equal tham
308.7(1097)^x=246(1155)^x
Dividing both sides by 246
1.254878(1097)^x=(1155)^x
Dividing both sides by (1097)^x
1.254878=(1155÷1097)^x
X=4.406 decades
X=44 years
The numerical increase in the count or number of people or things is known as population growth
The time when there will be on average, one vehicle per person is the year 2054
The reason the above value is correct is as follows:
The known parameters are;
The number of vehicles (cars and trucks) in 2010 = 246 million
The number people in the United States in 2010 = 308.7 million
The percentage by which the number of vehicles grew per decade = 15.7%
The percentage by which the population is growing per decade = 9.7%
Required:
The time when one vehicle per person on average
Solution:
Let the t, represent the number of 10 years at which there is one vehicle per person on average, we have;
[tex]246 \times \left(1 + \dfrac{15.5}{100} \right)^t = 308.7 \times \left(1 + \dfrac{9.7}{100} \right)^t[/tex]
[tex]\dfrac{308.7}{246} =\dfrac{\left(1 + \dfrac{15.5}{100} \right)^t}{\left(1 + \dfrac{9.7}{100} \right)^t} = \left(\dfrac{1 + \dfrac{15.5}{100} }{1 + \dfrac{9.7}{100} \right)} \right)^t[/tex]
[tex]\ln\left(\dfrac{308.7}{246} \right) =ln \left(\dfrac{1 + \dfrac{15.5}{100} }{1 + \dfrac{9.7}{100} \right)} \right)^t[/tex]
[tex]t = \dfrac{ \ln\left(\dfrac{308.7}{246} \right) }{ln \left(\dfrac{1 + \dfrac{15.5}{100} }{1 + \dfrac{9.7}{100} \right)} \right)} \approx 4.407[/tex]
The number of decades there will on average, one vehicle per person, t ≈ 4.407 decades
Therefore;
The number of years there will on average, one vehicle per person, n = 10 × t, which gives;
n ≈ 10 years/decade × 4.407 decades = 44.07 years
The number of years there will be on average, one vehicle per person is approximately 44 years
Therefore, the year when there will be on average, one vehicle per person is approximately 2010 + 44 = The year 2054
Learn more about population growth rate here:
https://brainly.com/question/23102091
