Population

The town has 65,000 inhabitants. 40 years ago, there were 157,000. How many people will live in a city in 10 years if the population's average rate is as in previous years?

Correct result:

x =  52139

Solution:

$$\begin{gathered} n_1=n_2\cdot q^{40} \\ \ln n_1=\ln n_2+40\cdot \ln q \\ \ln q={\displaystyle \frac{\ln 65-\ln 157}{40}} \\ \ln q=-0.0220464633863 \\ q=e^{-0.0220464633863}=0.978194783753 \\ p=-2.18\mathrm{\%} \\ x=65000\cdot q^{10}=65000\cdot 0.978194783753^{10} \\ x=52139 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Population
  What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
• Demographics
  The population grew in the city in 10 years from 30000 to 34000. What is the average annual percentage increase of population?
• Population growth
  How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
• Annual growth
  The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%?
• The city 3
  The city has 22,000 residents. How long it is expected to have 25,000 residents if the average annual population growth is 1.4%?
• Annual interest
  A loan of 10 000 euro is to be repaid in annual payments over 10 years. Assuming a fixed 10% annual interest rate compounded annually, calculate: (a) the amount of each annual repayment (b) the total interest paid.
• Microorganisms
  The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
• The crime
  The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2025.
• Compound interest
  Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?
• Investment
  1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
• The city
  At the end of 2010 the city had 248000 residents. The population increased by 2.5% each year. What is the population at the end of 2013?
• What is
  What is the annual percentage increase in the city when the population has tripled in 20 years?
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Radioactive material
  A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
• Bank
  Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
• Volume of wood
  Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
• Account operations
  My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?