# Exponential function + geometric progression - examples

1. Crystal
Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g?
2. Demographics
The population grew in the city in 10 years from 42000 to 54500. What is the average annual percentage increase of population?
3. Deposit
If you deposit 959 euros the beginning of each year, how much money we have at 2.1% (compound) interest after 19 years?
4. Loan
Apply for a \$ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
5. Sequence
Calculate what member of the sequence specified by ? has value 86.
6. 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?
7. Interest
Calculate how much you earn for 10 years 43000 deposit if the interest rate is 1.3% and the interest period is a quarter.
8. Half life
Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes.
9. 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.
10. The city 2
Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%?
11. 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?
12. 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%.
13. Population
What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
14. Sequence - 5 members
Write first five members of the sequence ?
15. Saving 9
An amount if \$ 2000 is invested at an interest of 5% per month. if \$ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumula
16. 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?
17. Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
18. 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.
19. Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
20. 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?

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