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An exponential function is given by the formula:
[tex]f(x)=a\cdot b^x[/tex]where a and b are numbers. b is always positive
We have that there are two ways of obtaining a decreasing exponential function:
1. if a is negative
2. if 0 < b < 1
We have that we have an increasing function if and only if
a is positive and b is higher than 1, b > 1
We have that:
In h(x) = 7 · 0.9ˣ
a = 7 and b = 0.9
Since 0 < 0.9 < 1, then it is a decreasing function.
In k(x) = 10 · (3/5)ˣ
a = 10 and b = 3/5 = 0.6
Since 0 < 3/5 < 1, then it is a decreasing function.
In n(x) = 4 · (7/6)ˣ
a = 4 and b = 7/6 = 1.166...
Since a is positive and b is higher than 1: 1 < 1.166...,
then it is an increasing function.
In p(x) = -10 · 8ˣ
a = -10 and b = 8
Since a is negative, then it is a decreasing function.
In j(x) = 2 · (1 + 0.03)ˣ
a = 2 and b = 1 + 0.03 = 1.03
Since a is positive and b is higher than 1: 1 < 1.03,
then it is an increasing function.
In g(x) = 0.25 · 6ˣ
a = 0.25 and b = 6
Since a is positive and b is higher than 1: 1 < 6,
then it is an increasing function.
In f(x) = 5 · 2ˣ
a = 5 and b = 2
Since a is positive and b is higher than 1: 1 < 2,
then it is an increasing function.
In m(x) = 3 · 4ˣ - 5
a = 3 and b = 4
Since a is positive and b is higher than 1: 1 < 4,
then it is an increasing function.
