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Exponential and Logarithmic Applications
Growth and Decay Formulas
Exponential Growth or Decay: A(t) = A0bt
 1
Half-life: A t   A  
0 2
t
k
 
 r
Compound Interest: A(t) = P 1  
 n
nt
Continuously Compounded Interest: A(t) = Pert
Continuous Growth or Decay: A(t) = A0ekt
1. Upon graduating from college, Ashley took a job with a
starting salary of $40,000. She can expect a 6% raise in pay
each year. In notes 7-6 we found by graphing that after 6.959
years Ashley would be earning $60,000/year. Confirm this
result algebraically.
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2. Living organisms can be dated by the amount of carbon-14
present at time t compared to the amount present when the
organism was alive. The half-life of carbon 14 is 5730 years.
How long would it take for a 185 microgram sample of carbon14 to decay to 24 grams? (Round to the nearest 100 years.)
3. Suppose a culture of bacteria is put in a petri dish and grows
continuously. The culture doubles every 4 hours.
a) Write a function to model the continuous growth of the
bacteria.
b) If the initial amount of bacteria is 100, how many bacteria will
there be in 15 hours? (Round to the nearest whole number.)
c) When will the bacteria count be 350,000?
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4. Suppose you plan to invest $2500 at an annual rate of 7.5%.
a) How much will you have in the account after five years if the
balance is compounded quarterly?
b) How long will it take to have $10,000 if the balance is
compounded quarterly?
c) How long will it take to have $10,000 if the $2500 is
compounded continuously?