Exponential and Logarithmic Functions and Equations

Exponents

100

Simplify. Leave no negative exponents.

(2x^3y^-1z^2)/(4xy^2z^5)

(x^2)/(2y^3z^3)

200

Simplify. Leave no exponents negative.

(3x^-2yz^4)(2x^3y^-2z)

(6xz^5)/y

300

Simplify. Leave no exponents negative.

(3x^4y^-1z^3)^0((x^3y^-1z^4)((2x^5)/(5z^2)))^2

(4x^16z^4)/(25y^2)

Exponential Models

100

The squirrel population at Concord High School is 1000 at the beginning of the year on August 1. The population INCREASES at a rate of 8.25% MONTHLY.

A. Find the exponential function that models the squirrel population as a function of time (in months)

B. Find the squirrel population at the end of the year on June 1.

P(t)=1000(1.0825)^t

P(10)=1000(1.0825)^10

2209.42

200

You deposit $500 into a savings account the pays 2.73% annual interest compounded quarterly. 

A. Find the exponential function that models this situation.

B. How much money will you have in the account in 5 years?

A.

A(t)=500(1+.0273/4)^(4*5)

300

The lab has a 1000g sample of a material with a 12year half-life. 

A. Find the exponential function that models the situation.

B. Find the amount of the sample that will be left after 20 years.

A.  A(t)=1000(.5)^(t/12) 

B.  A(20)=1000(.5)^(20/12) 

      A(20)=314.98 g 

Equivalent Expressions

100

Find the equivalent LOGARITHMIC EXPRESSION.

2^6=64

log_2 64=6

200

Find the equivalent EXPONENTIAL EXPRESSION:

log_5(1/5)=-1

 5^-1=1/5 

300

Find the equivalent EXPONENTIAL EXPRESSION.

log .001=-3

 10^-3=1/1000=.001 

Evaluating Logs

100

Simplify:

log_3 9

2

200

Simplify:

log_7 (1/49)

-2

300

Simplify:

log .1

-1

Log Properties

100

EXPAND:

log_3 4x

log_3 4 * log_3 x

200

EXPAND:

log_8 ((2x)/5)

 log_8 2 + log_8 x - log_8 5 

300

EXPAND: log (3x)^2 

2log3+2logx