Half life of exponential....thanks (1 Viewer)

[lanvins]

The populations of Cook Islands and Niue in the South Pacific has been decreasing at an average rate of 2½% per year over the last 5 years. If the combined population was 23400 in 2007

Define all terms clearly.
a) General formula for Half-Life, knowing the rate of change:

For the given rate of change of 2½%: Exact half life =.............. years

b) Devise the general formula for the RATE OF GROWTH/DECAY of any exponentially growing or decaying quantity, given the half-life. State the formula specific to the population of Cook Islands and Niue. Define all terms clearly.

General formula for rate of change, knowing the half-life:
From the observed half-life, the rate of change in the population =

 

[Uncle]

T is the time elapsed.
k is the proportionality constant.
0.5 is half of something, usually half-life.

e^kT = 0.5

ln(e^kT) = ln(0.5)

Now, ln (0.5) = - ln(2) from logarithmic laws (Don't forget the minus sign)

Then the general formula is:

kT = - ln(2)