Exp. Functions
Growth or decay:
f(x)=0.3(5)^x
Growth
What's RoC, if f(x) passes through (1,4) and (3,16)
6
2, 6, 18, \ldots
a=2,b=3
3^x to 27^x
Horizontal dilation
Increasing/Decreasing:
f(x)=-7(7)^x
Decreasing
Common ratio for
[[x\rightarrow, 11, 13, 15],[y\rightarrow, 8,16,32]]
\sqrt{2}
7,3.5,1.75,\ldots
a=7,b=0.5
8^x to \frac{1}{8^x}
Reflection across the y-axis
Concavity?
8(\frac{1}{9})^x
Concave up
The 3rd term of a geo. sequence is 5, and the 5th term is 20. Find the 6th term.
40
1,\sqrt{2},2,\ldots
a=1,b=\sqrt{2}
4^x to -4\cdot{4^x}
Reflection across the 𝑥-axis and shift left 1
Growth/decay?
[[x\rightarrow, 0, 1, 2],[y\rightarrow, 5, 1, 0.2]]
Decay
What's a_5
[[n\rightarrow, 0, 2, 4],[a\rightarrow, 1024, 6400, 40000]]
100000
[[x\rightarrow, 0, 1, 2],[y\rightarrow, 5, 1, 0.2]]
a=5,b=0.2
f(x)=7^x to g(x)=\frac{f(x)}{49}
Shift right 2 units
\lim_(x->oo)7(0.1)^x
0
The exp. function that passes through (0,3) and (4,27)
y=3(\sqrt{3})^x
[[x\rightarrow, 0, 2, 4],[y\rightarrow, 8, 2, 0.5]]
a=8,b=0.5
f(x)=5^x to g(x)=-25\cdot f(x)
Reflection across the 𝑥-axis and shift left 2