Scenario 1 Glenda Jones is seeking to invest a sum of money

Scenario 1:  Glenda Jones is seeking to invest a sum of money into an account set aside for her newborn grandson. She has talked to various financial institutions and has decided to invest in a bank that provides continuously compounding interest.

Scenario 2:  Samuel Richardson is in a chemistry course where he is studying carbon dating. After a plant or animal dies, the radiocarbon disintegrates. Scientists can determine the age of the remains by comparing the amount of radiocarbon with the amount present in lving plants and animals. The amount of radiocarbon present after t years is modeled using the above function.

Solution

Solution-

Scenario 1: When money continuously compounded, It increases with time exponentially, So it is a case of exponential growth and here k is positive.

For example - An amount $4000 compounding continuously at a rate of 8% for 5 years.

Here k = 0.08

Scenario 2. In carbon dating we check the amount of radiocarbon present after t years, Carbon decreases with time exponentially so it is a case of exponential decay and here k is negative.

For example - Carbon is decaying at rate of 4% per year

Here k = -0.04