COMPOUNDED CONTINUOSLY WORD PROBLEMS WORKSHEET

Problem 1 :

Find the present value of $5000 to be received in 2 years if the money can be invested at 12% annual interest rate compounded continuously.

Solution

Problem 2 :

An investment earns at an annual interest rate of 4% compounded continuously. How fast is the investment growing when its value is $10,000?

Solution

Problem 3 :

One thousand dollars is deposited in a savings account at 6% annual interest rate compounded continuously. How many years are required for the balance in the account to reach $2500?

Solution

Problem 4 :

In a certain neighbourhood of Vancouver, property values tripled from 2001 to 2011. If this trend continues, when will property values be five times their 2001 level? Answer property values behave as if the annual investment rate is compounded continuously.

Solution

Problem 5 :

Suppose that the present value of $1000 to be received in 5 years in $550. What rate of interest, compounded continuously, was used to compute this present value?

Solution

Problem 6 :

Investment A is worth $70 thousand, and is growing at a rate of 13% per year compounded continuously. Investment B is worth $60 thousand is growing at a rate of 14% per year compounded continuously. After how many years will the two investments have the same value?

Solution

Problem 1 :

Madeline decided to invest her $500 Christmas money. She found a bank offering 5.5% compounded continuously. What will be her ending balance after investing for 4 years?

Solution

Problem 2 :

Your parents starts a college fund when you enter kindergarten at age 5. They invest $14,000 in an account that earns 0.8% annual interest compounded continuously.

If you are 18 years old when you enter college, how much money is available in your college find at that time, to the nearest dollar?

Solution

Problem 3 :

The population P (in thousands), Nevada can be modeled 

P = 134𝑒^kt

where t is the year with t = 0, corresponding to the year 1990. In 2000 the population was 18000.

• Find the value of k for the model. Round the answer for four decimal places.
• Use the model to predict the population in 2010.

Solution

Problem 4 :

The population (in thousands) of Las vegas, Nevada by

P = 258000𝑒^kt

where t is the year with t = 0 corresponding to the year 1990. In 2000 the population was 478000.

• Find the value of k for the model. Round your decimal nearest four digits.
• Use the model to predict the population in 2010.

Solution

Problem 5 :

The initial bacterium count in the culture is 500. A biologist later makes a sample count of bacteria in the culture and finds that the relative rate of growth is 40% per hour.

• Find a function that models the number of bacteria after t hours. y = a𝑒^kt 
• What is the estimated count after 10 hours.

Solution

Problem 6 :

A certain breed of rabbit was introduces onto a small island about 8 years ago. The current rabbit population on the island is estimated to be 4100, with a relative growth rate of 55% per year.

• What was the initial size of the rabbit population, use y = A𝑒^kt
• Estimate the population 12 years from now.

Solution

Problem 7 :

The population of the world in 2000 was 6.1 billion and the estimated related growth rate was 1.4% per year. If the population continues to grow at this rate, when will it reach 122 billion ? y = A𝑒^kt

Solution

Problem 8 :

A culture starts with 8600 bacteria. After 1 hour the count 10000.

Find the function that models the number of bacteria after t hours. y = A𝑒^kt

• Find the bacteria after 2 hours.
• After how many hours the number of bacteria will become double.

Solution