MP 4 QUARTERLY REVIEW

MIXED BAG

1

Find the inverse equation of 

f(x) = 2x - 7

f^-1(x) = (x + 7)/2      

2

Find the inverse equation of 

f(x) = 5x + 2

f^-1(x) = (x - 2)/5      

3

Rewrite 

log₅ 15 = x + 7 in 

exponential form

5^x+7 = 15

4

Which of the following represent exponential equations?

f(x) = x²         f(x) = x         

f(x) = 2^x+5       f(x) = log₇x     

f(x) = 3^x         f(x) = 3x^1/3

 f(x) = 2^x+5   and   f(x) = 3^x  

5

Melanie invested $15,000 in an account that earns an annual interest rate of 3.5%. Find the balance in Melanie's account after 8 years, if the interest is compounded monthly.

$19,838.86

GROW UP!

1

Does f(x) = -5(2/3)^x  represent exponential growth or decay?

decay, because  2/3 < 1

2

Does f(x) = (9/4)^x  +  7 represent exponential growth or decay?

growth, because 9/4 > 1

3

Which exponential function represents growth?

f(x) = 2(3)^x-3  or  

f(x) = (1/3)^x

f(x) = 2(3)^x-3

4

The graph of 

f(x) = 1/2(3)^x - 7 is 

vertically _?_ (stretched or compressed) 

by a factor of _?_

compressed by a factor of 1/2

5

The initial population of lady bugs in a garden is 325 and increases at the rate of 2.5% per year. Find the final population of lady bugs after 4 years.

359

DON'T TOUCH THIS!

1

Given f(x) = 4^x - 3 state the following:

a) asymptote

b) range using interval notation

a) y = -3

b) (-3, infinity)

2

Given f(x) = 2^x+5 + 6 state the following:

a) asymptote

b) range using interval notation

a) y = 6

b) (6, infinity)

3

A graph represents exponential decay if it _?_

a) increases from left to right

b) doesn't have an asymptote

c) decreases from left to right

c) decreases from left to right

4

The asymptote of f(x) = 5^x+3 - 4 is shifted _?_ when compared to that of its parent function, f(x) = 5^x.

a) 3 units right

b) 4 units down

c) 4 units left

b) 4 units down

5

The y-intercept for the graph of 

f(x) = 3^x+2 - 6 is located 

at (?,?).

(0,3)

ALL ABOUT THAT BASE

1

Solve 9^2x-5 = 9^6x-13 without using a calculator

x = 2

2

Solve 4^x+7 = 64^x

x = 7/2

3

Rewrite 

log₅ 12 = x + 3 in exponential form

5^x+3 = 12

4

Solve 

log₆ (x + 9) = 2

x = 27

5

Solve 

log₄(x + 5) + log₄6 = log₄(4x + 2)

no solution  

(because x = -14 does not satisfy the log equation)

DAILY LOG

1

Evaluate log₆ 216 without using a calculator 

3

2

Given 5^x = 12

a) rewrite in log form

b) solve, round answer to nearest hundredth

a) log₅ 12 = x

b) 1.54

3

Solve  16^x = 7  

Round answer to the nearest thousandth.

.702

4

Condense   

4log₃2 + log₃5  into a single log

log₃80

5

Expand log₈ (xy⁴)/z² using log properties

log₈x + 4log₈y - 2log₈z