Download Pre Calculus (A)

Pre Calculus (A)
Exponential Growth and Decay – Applications
Name: ___________________________
Law of Uninhibited(continuous) Growth/Decay: N  N0 e kt , where
N = final population
N0 = initial population
k = continuous growth/decay rate
t = time
Example 1 Bacterial Growth
A colony of bacteria grows according to the law of inhibited growth according to the function N(t) = 100e0.045t, where
N is measured in grams and t is measured in days.
a) Determine the initial amount of bacteria.
b) What is the growth rate of the bacteria?
c) What is the population after 5 days?
d) How long will it take for the population to
reach 140 grams?
e) What is the doubling time for the population?
Example 2 More Bacterial Growth
A colony of bacteria increases according to the law of uninhibited growth.
a) If the number of bacteria doubles in 3 hours, find the function that gives the number of cells in the culture.
b) How long will it take for the size of the colony to triple?
Example 3 Age Estimation
Traces of burned wood along with ancient stone tools in an archaeological dig in Chile were found to contain
approximately 1.67% of the original carbon-14.
If the half-life of carbon-14 is 5,600 years, approximately when was the tree cut and burned?
Example 4 More Radioactive decay
Iodine-131 is a radioactive material with a half-life of 8 years.
a) What is the decay rate of iodine-131?
b) If there are 28 grams of iodine-131 present in a sample today, how much will remain in 6 months?
c) How long will it take until 10 grams remains?