Algebra 1 Unit 6

Simplifying Exponential Expressions

100

xy^4*x^(-5)y

y^5/x^4

200

(n^(-6))/(m^0n^(-9))

n^3

300

((4a^4)/(b^2))^(-3)

b^6/(64a^12)

400

-(32)^(1/5)

-2

Key Features of Exponential Functions

100

Compared to the graph of the parent function f(x), the graph of g(x) is a vertical stretch by a factor of ___.

f(x)=5^x

g(x)=3(5)^x

3

200

Compared to the graph of the parent function f(x), the graph of g(x) is a vertiacal shift 3 units ____.

f(x)=5^x

g(x)=5^x+3

up

300

Compared to the graph of the parent function f(x), the graph of g(x) is a horizontal shift 3 units ____.

f(x)=5^x

g(x)=5^(x+3)

left

400

Identify the Domain AND Range of f(x).

f(x)=3(5)^x

Domain: All Real Numbers

Range: y>0

Exponential Growth and Decay

100

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function f(x). Evaluate the function when t=5. Round your answer to the nearest hundredth.

f(x)=15(1.07)^t

a=15

r=7%

f(5)=21.04

200

Your starting annual salary of $35,000 increases by 4% each year. Write a function that represents your salary y (in dollars) after x years.

y=35000(1.04)^x

300

You purchaced a car in 2010 for $32,000. The value of the car decreses by 12% annually. Write a function that represents the value of the car y (in dollars) after x years. THEN find the value of the car in 2024.

y=32000(0.88)^x

The car would be worth $5,344.50 in 2024. 

400

You deposit $750 into an account that earns 6.5% annual interest compounded quarterly. Write a function that represents the balance y (in dollars) after x years. 

y=750(1+0.065/4)^(4x)

Solving Exponential Equations

100

5^(x+6)=1/625

x=-10

DOUBLE POINTS!!!!

200

3^x=1/243

x=-5

300

2^(4x-7)=8^(2x+1)

x=-5

DOUBLE POITNS!!!

400

512^(x+2)=8^(2x-1)

x=-7

Geometiric Sequences

100

Write the next three terms of the geometric sequence:

5, 20, 80, 320, __, __, __, .....

1280, 5120, 20480

DOUBLE POINTS!!!

200

Write an equation for the n-th term of the geometric sequence:

1400, 700, 350, 175, ...

a_n=1400(1/2)^(n-1)

DOUBLE POINTS!!!

300

Identify the first term a₁, and the common ratio r. Write the equation for the nth term a_n of the geometric sequence and find a₂₀.

54, 72, 96, 128, ....

a₁=54

r=4/3

a_n=54(4/3)^(n-1)

a_20=12,771.14

400

Identify the first term a₁, and the common ratio r. Write the equation for the nth term a_n of the geometric sequence and find a₂₀.

128, 32, 8, 2, 0.5, .....

a₁=128

r=1/4

a_n=128(1/4)^(n-1)

a_20=1/2147483648