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

6 months ago  Like

Next similar math problems:

• Exponential decay
  A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?
• Population
  The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years?
• Pilsen circus
  The arrival of the circus in Pilsen was seen in the morning at 08:00 by a citizen of the city. He passed this information on 08:15 to three other residents of the city. Each of these three people then informed the other three residents at 08:30, and again
• 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?
• 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
• Crystal
  Crystal grows every month 1.2 promile of its mass. For how many months to grow a crystal from weight 177 g to 384 g?
• 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.
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• 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?
• 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?
• Future value
  Suppose you invested $1000 per quarter over a 15 years period. If money earns an anual rate of 6.5% compounded quarterly, how much would be available at the end of the time period? How much is the interest earn?
• Investment 2
  Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi
• Savings
  The depositor regularly wants to invest the same amount of money in the financial institution at the beginning of the year and wants to save 10,000 euros at the end of the tenth year. What amount should he deposit if the annual interest rate for the annua
• Pilsen Region
  Between 2000 and 2001, 14 per mille of the population decreased in the Pilsen Region. In 2000, the Pilsen Region had 551281 inhabitants. If the declining trend continues the same (i. E. , 14 per mille of inhabitants per year), how many inhabitants will th
• 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?
• Precious metals
  In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3 4
• Loan 5
  Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan? C