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Continuous vs Non-Continuous Exponential Equations.doc
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Exponential growth or decay can be modeled using either the Continuous or NonContinuous form of the Exponential equation.
Exponential Equation
Continuous Exponential Equation
P  P0 a t
P  P0 e kt
Examples:
a) A population of 300 is increasing at a continuous rate of 5%: P  300e
0.05 x
c) A population of 300 is decreasing at a continuous rate of 5%: P  300e
0.05 x
b) A population of 300 is increasing at a rate of 5%. (non-continuous) P  300(1.05)
x
d) A population of 300 is decreasing at a rate of 5%. (non-continuous) P  300(0.95)
x
Questions:
Write an exponential equation for each situation described. (For the problems below use
the non-continuous form unless continuous growth or decay is explicitly stated.)
1) A bank account is started with a $1,000 deposit and the interest rate is 3%
compounded continuously.
2) A bank account is started with a $1,000 deposit and the interest rate is 3%
compounded annually.
3) The population of bacteria is 5000 and is decreasing continuously at a rate of 1.2%.
4) The population of bacteria is 5000 and is decreasing at a rate of each hour 1.2%.
5) A sample of an isotope has a half-life of 50 years. Write an equation for the quantity,
Q, left after t years, if the initial amount is Q0.
6) The population of birds in an area is 2,000 and is increasing at a rate of 8% every 2
years.
7) The population of bees is 50,000 and is decreasing at continuous rate of 4.5% per
year.
8) A car was purchased for $25,000 and depreciates by 18% each year.
9) You invest $5,000 in a bank CD with 1.8% interest compounded daily.
10) The value ‘V’ of an investment is doubling every 10 years.
Write an equation for the value after t years, if the initial amount is V0.
11) The thickness of a piece of paper doubles after each fold. Write an equation for the
thickness after x folds, if the initial thickness is 0.005 inches.
12) The population of ants in world is 50,000,000,000,000,000 and is increasing
continuously at a rate of 0.5%.