Exponents and Exponentials

Exponent rules 1

100

Simplify: x²*x³

x⁵

200

Simplify: x^-12

1/x¹²

300

Simplify (xy²)⁵1234⁰

x⁵y¹⁰

400

Which expression is equivalent to: (x^2/3)⁴

x^8/3

500

Simplify: x⁵y² / (x³y)

x²y

Exponent Rules 2

100

Simplify: x⁵/x²

x³

200

Simplify: (x¹³)²

x²⁶

300

Simplify x⁴y³z³/x²yz¹⁰

x²y²/z⁷

400

Which expression is equivalent to: (x^5/9)²

x^10/9

500

Simplify (10a⁰b³c²⁰)(2a¹⁵b^-25c⁰) 

20a¹⁵c²⁰/b²²

Exponential Functions 1

100

Which letter represents the INITIAL VALUE in an exponential function? a(b)^x

a

200

What is the initial value in the function: 123(0.3)^x

123

300

Write an exponential function that represents investing $500 into a bank account that has a yearly percent increase of 10%.

y=500(1.10)^x

400

Given the function: v(d)=575(0.65)^x identify the:

- initial value

-increasing or decreasing?

-rate increase or descrease? _%

-575

-decreasing

-35%

500

Write a exponential function to represent the following: A person buys a new car for $28,000. Each year, the car loses 15% of its value due to depreciation. Let x represent the number of years since the car was purchased.

y=28000(0.85)^x

Exponential Functions 2

100

Which letter represents the RATE in an exponential function? a(b)^x

b

200

A cars value is represented as C=20000(0.80)^x overtime where x represents the number of years after being bought brand new. What will the value of the car be after 4 years?

$8192

300

What is the growth rate in the function 145(2)^x

2

400

A person invests $5,000 into a mutual fund that earns an average annual return of 6%, compounded once per year. Let x represent the number of years the money is invested.
Write a function that models the value of the investment after x years, and use it to find how much the investment will be worth after 10 years. Round to the nearest cent.

y=5000(1.06)^x

$8954.24

500

In a lab, a scientist watches how fast bacteria replicates. The data she records can be modeled by the function, b(t), where b is the total number of bacteria and t is time measured in hours. The initial amount of bacteria was 200 and grew at a rate of 50%, Write an exponential function to represent this. How many bacteria will be present after 7 hours. Round to the nearest whole number. 

b(t)=200(1.5)^x

3417 

Exponential Functions 3

100

Given this equation: 6(1.34)^x

The function is inccreasing at a rate of ___%

34%

200

Given this equation: 200(0.30)^x

The function is decreasing at a rate of ___%

70%

300

Given this equation: 1134(0.98)^x

The function is decreasing at a rate of ___%

2%

400

Given this equation: 981(1.345)^x

The function is increasing at a rate of ___%

34.5%

500

Given this equation: 6(0.75)^x

The function is decreasing at a rate of ___%

25%