# MATA02H3 Lecture Notes - Asymptote, Richter Magnitude Scale, Logarithm

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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.