Please help me with this.

Question

Find the half-life of a radioactive substance that decays at a continuous rate of 16% per minute,

Round your answer to three decimal places.

The half-life is minutes.

Answer 1

A = Amount

A0 = Initial Amount

t = time in minutes

A = A0( 1 + r )^(t) Exponential Growth

A = A0( 1 - r )^(t) Exponential Decay

Here:

A = A0( 1 - 0.16)^(t)

A = A0( .84 )^(t)

When the Amount is equal

to half the original Amount,

we have:

(1/2)*A0 = A0( .84 )^(t) Divide both sides by A0

(1/2) = ( .84 )^(t)

ln(1/2) = t*ln( .84 )

t = [ ln(.5) ] / [ ln(.84) ]

t = 3.9755303

t = 3.976 minutes