Jeopardy - Exponential Equations & Logs - Alg2

Exponential Graphs

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.

200

Write the END BEHAVIOR of this graph.

x->oo f(x)->oo

x->-oo f(x)->3

300

Write the equation of the exponential graph.

y=4/9(3/2)^x

Exponential Equations

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.

200

Write the exponential equation for the table below.

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 2^3x=2⁶.  That means 3x=6, so x=2.

400

Solve the exponential equation WITHOUT using logarithms or your calculator.

x=9

Since 27^x+3=(3³)^(x+3) we can rewrite the equation as 3^4x=3^3x+9.  That means 4x=3x+9, so x=9.

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.

Logarithms

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

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.

300

Write the logarithm in EXPONENTIAL form.

7^-2=1/49

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

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)

Talk the Talk

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