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Section 6.5 : Applications

1. We have $10,000 to invest for 44 months. How much money will we have if we put the money into an account that has an annual interest rate of 5.5% and interest is compounded
   1. quarterly
   2. monthly
   3. continuously
   Solution
2. We are starting with $5000 and we’re going to put it into an account that earns an annual interest rate of 12%. How long should we leave the money in the account in order to double our money if interest is compounded
   1. quarterly
   2. monthly
   3. continuously
   Solution
3. A population of bacteria initially has 250 present and in 5 days there will be 1600 bacteria present.
   1. Determine the exponential growth equation for this population.
   2. How long will it take for the population to grow from its initial population of 250 to a population of 2000?
   Solution
4. We initially have 100 grams of a radioactive element and in 1250 years there will be 80 grams left.
   1. Determine the exponential decay equation for this element.
   2. How long will it take for half of the element to decay?
   3. How long will it take until there is only 1 gram of the element left?
   Solution