Question

The rate of change of a bacteria (N) with respect to time is directly proportional to itself. When t=0, N=500. When t=4, N=3000. How many bacteria will be present when t=8?
Carbon-14 has a half-life of 5715 years. Find the rate of decay, if the initial amount of carbon-14 is 10 units.

Please explain (step by step is preferred)

Answer 1

Fine the average rate of change by the difference in N over the difference in T:

3000 - 500 / 4-0 = 2500 / 4 = 625

This means for every 1 T, N = 625.

Now multiply 625 by 8:

625 x 8 = 5000

When T = 8 N = 5,000

The decay rate can be found by dividing -ln(2) by the half life.

Decay rate = -ln(2) / 5715 = -0.00012