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.

Correct result:

n =  12

Solution:

$$\begin{gathered} q={\displaystyle \frac{11}{10}}=1.1 \\ {q}^n=3 \\ n\cdot \ln q=\ln 3 \\ {n}_1=\ln (3)\mathrm{/}\ln (q)=\ln (3)\mathrm{/}\ln (1.1)\doteq 11.5267 \\ n=\lceil n_1\rceil =\lceil 11.5267\rceil =12 \end{gathered}$$

Try another example

Showing 1 comment:

Math student

I can't understand

9 months ago  Like

Next similar math problems:

• 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?
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Demographics
  The population grew in the city in 10 years from 30000 to 34000. What is the average annual percentage increase of population?
• Population
  What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
• Geometric sequence 3
  In geometric sequence is a₈ = 312500; a₁₁= 39062500; s_n=1953124. Calculate the first item a₁, quotient q and n - number of members by their sum s_n.
• Annual growth
  The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%?
• 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?
• 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.
• Growth of wood
  The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
• 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?
• Radioactive material
  A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
• GP members
  The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
• Sequence - 5 members
  Write first five members of the sequence ?
• Geometric sequence
  In the geometric sequence is a₄ = 20 a₉ = -160. Calculate the first member a₁ and quotient q.
• 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?
• Retirement annuity
  How much will it cost to purchase a two-level retirement annuity that will pay $2000 at the end of every month for the first 10 years, and $3000 per month for the next 15 years? Assume that the payment represent a rate of return to the person receiving th
• To the cinema
  Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in