MATA02H3 Lecture Notes - Asymptote, Richter Magnitude Scale, Logarithm

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17 Nov 2011
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Graphs of Exponential Functions:
2^x 3^x 4^x 5^x
They all go through the point (0,1)
The y-values all grow quickly to the right of (0,1)
The y-values get smaller and nearer to 0 to the left of (0,1). The x-axis is the asymptote.
The larger the base, the quicker the y-value to the left approach the asymptote.
The base of 1 is a horizontal line.
(1/2)^x (1/3)^x (1/4)^x (1/5)^x
-they all go through the point (0,1)
-the y-values all grow quickly to the left of (0,1)
-the y-values get smaller and nearer to 0 to the right of (0,1). The x-axis is the asymptote.
-the y-values are always positive.
-They are flipped on the y-axis
APPLICATIONS OF EXPONENTIAL FUNCTIONS
The formula for exponential doubling is N(t) = N02^t/d
N(t)- the number at the time t
N0- the initial number or concentration at time 0.
2- because the population is doubling
t- time elapsed since measuring started (express this in the same units as d)
d- doubling period.
The formula for half life is:
C(t) = C0(1/2)^t/H
C(t)- the number at the time t
C0- the initial number or concentration at time 0.
2^-1 or 1/2- because the population is halving
t- time elapsed since measuring started (express this in the same units as H)
d- half life.
The formula for compound interest is:
A = P(1 + i)n
A- the amount the account will grow to
P- the principle amount originally invested
i- the annual interest rate
n- the number of years the principal is invested.
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