Exponential Graphs
Exponential Equations
Logarithms
Talk the Talk
100
Is this graph represent exponential GROWTH or DECAY?
EXPONENTIAL GROWTH
The outputs (y-values) are "growing" or getting larger in the negative direction. The outputs will approach negative infinity.
100
Does this exponential function model GROWTH or DECAY?
y=0.75(5/6)^x+3
DECAY
The common ratio (r) in this equation is less than 1 which indicated decay (the outputs are getting smaller by a factor of 5/6 for every increase of 1 in the input.
100
What is the OUTPUT of a LOGARITHMIC function?
an EXPONENT
Logarithms are the inverse of exponential functions and used when solving exponential equations where the exponent is unknown. The output of a logarithm is an exponent.
200
Write the END BEHAVIOR of this graph.
x->oo f(x)->oo
x->-oo f(x)->3
200
Write the exponential equation for the table below.
200
Estimate the value of log3 (90) WITHOUT a calculator.
xapprox4.1
Since 34=81 and 35=243, we can see x must be between 4 and 5. Since 90 is much closer to 81 than 243, we can estimate the value to be slightly over 4.
200
What are the restrictions on the BASE of an EXPONENTIAL function?
The base can be any positive number except 1.
0<base, base ne1
300
Write the equation of the exponential graph.
y=4/9(3/2)^x
300
Solve for the exponential equation WITHOUT using logarithms or a calculator.
2^(3x)=64
x=2
Since 26=64 we can rewrite the equation as 23x=26. That means 3x=6, so x=2.
300
Write the logarithm in EXPONENTIAL form.
7^-2=1/49
400
Solve the exponential equation WITHOUT using logarithms or your calculator.
x=9
Since 27x+3=(33)(x+3) we can rewrite the equation as 34x=33x+9. That means 4x=3x+9, so x=9.
400
y=log_3((x-5)/2)-4
The inverse of an exponential function is a logarithm. So rewrite the original function in logarithmic form by switching x and y and then isolating y.
500
f(-1)=27 and f(2)=1 are coordinates that can be found using an exponential equation. Find the equation that created these points.
f(x)=9(1/3)^x
Set up a system of equations. Isolate r or A and then use substitution to solve.
500
Solve for x WITHOUT a calculator.
x=-2 and 4
First write the equation in exponential form. Then use Algebra to isolate x.
2^3=(x^2-6x)/(1-x)