It is known that is the exponetial growth or decay function

It is known that

is the exponetial growth or decay function. Describe what you know about the variable k in the two following scenarios:

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

1)given the bank provides continuosly compounding interest.hence the interest rate depends on value of k.as exponential

2)here disintegration rate depends on k . like the rate of disintegration is directly proportional to amount present and the function arrives