eharetea

Use of exponents and logorithms to solve problems involving half-life and population growth.

Exponential growth and decay. Mathematics.

Date Created:Monday January 22nd, 2007 08:09 AM
Date Modified:Saturday August 02nd, 2008 12:15 PM

A(t) = Ae^kt

How long will it take to reach 140 grams of bacteria for N(t) = 100e^0.045t?

140 = 100e^0.045t
1.4 = e^0.045t
ln1.4 = 0.045t
ln1.4/0.045 = t

t ≈ 7.5 days


When will the population double?

2A = Ae^0.045t
200 = 100e^0.045t
2 = e^0.045t
ln2 = 0.045t
ln2/0.045 = t

t ≈ 15.4 days


Something found with 1.67% of the original amount of C-14. C-14 has a half-life of 5600 years. How old is it?

1/2(A) = Ae^k(5600)
1/2 = e^5600k
ln1/2 = 5600k
ln(1/2)/5600 = k

k ≈ -0.000124

0.0167A = Ae^-0.000124t
0.0167 = e^-0.000124t
ln0.0167 = -0.000124t
ln0.0167/-0.000124 = t

t ≈ 33,000 years