Algebra Chapter 7 Review

Exponential Equations

100

What is the general form for an exponential function with an asymptote at y=0

y=a·b^x

200

What is an asymptote? 

In this course, a line that a graph of a curve approaches but never meets. 

"A barrier" 

300

Find the expoential equation that:

Has an initial value of 2 and passes through the point (3,128)

y=2·4^x

400

Find the expoential equation that passes through the points (0,4) and (2,1) 

y=4(0.5)^x

500

Find the expoential equation that passes through (1,8) (7,512)

y=4·2^x

Fractional Exponents and Radicals

100

Rewrite using a fractional exponent.

³√x

x^1/3

200

Rewrite using a radical

x^10/3

³√x¹⁰

300

Rewrite using a fractional exponent.

⁵√x⁶

x^6/5

400

Rewrite using a fractional exponent.

√x⁷

x^7/2

500

Rewrite using a radical, then evaluate the expression.

27^2/3

You must correctly answer both parts to earn the points.

Radical: ³√27² or (³√27)²

(³√27)² = (3)²=9

Generic Rectangles

100

Rewrite the product as a sum using a generic rectangle.

(4x+2)(7x+1)

28x²+18x+2

200

Rewrite the product as a sum using a generic rectangle.

(2x-1)(5x-2)

10x²-9x+2

300

Rewrite the product as a sum using a generic rectangle.

(x + 2)(x + y − 2)

x²+xy+2y-4

400

Rewrite the product as a sum using a generic rectangle.

(3x-9)²

9x²-54x+81

500

Rewrite the product as a sum using a generic rectangle.

3(2x-1)²

12x²-12x+3

Diamond Problems

100

Solve the diamond problem

   t

-11   -9

   b

t= 99 and b=-20

200

Solve the diamond problem

 t

-7   r

 10

r=13 and t= -91

300

Solve the diamond problem

   t

25   1/2

   b

t = 25/2  and b=25.5

400

Solve the diamond problem

 26

-2   r

 b

r = -13

b= -15

500

Solve the diamond problem

 18

L   r

 -9

L=-3 and r=-6 OR flipped :)

Word Problems

100

The Harnapps and the Curies are going to the Pizza Palace for dinner. The Harnapps order 3 slices of pizza and 3 colas and have a bill that totals $15. The Curies order 4 slices of pizza and 3 colas and have a bill that totals $18.What is the cost of a slice of pizza and a cola?

Let p = cost of pizza

Let c = cost of cola

3p+3c=15

4p+3c=18

200

There are 21 animals on Farmer Cole’s farm – all sheep and chickens.  If the animals have a total of 56 legs, how many of each type of animal lives on his farm?  

Let s = sheep

Let c = chickens

c+s=21

2c+4s=56

300

A piggy bank of coins has quarters and dimes totaling $2.90. If there are 8 more dimes than quarters, how many of each coin is in the piggy bank?

Let q = number of quarters

Let d = number of dimes

.25q+0.10d=2.90

q+10=d (OR d-10=q)

400

Ariel bought several bags of caramel candy and taffy. The number of bags of taffy was 5 more than the number of bags of caramels. Taffy bags weigh 8 ounces each, and caramel bags weigh 16 ounces each. The total weight of all of the bags of candy was 400 ounces. How many bags of candy did she buy?

Let t = bags of taffy

Let c = bags of caramels

8t+16c=400

c+5=t (or t-5=c)

500

The length of a rectangle is 4cm longer than the width. The perimeter is 80 cm. Find the length and the width.

Let L = length

Let w = width

w+4 = L

2(L+w)=80