Formulate the Formula
Real-World Exponentials
Rate It and Relate It!
Radical Reasoning
Exponent Express
100

The population of a town grows by 5% annually. If the population was 15,000 people initially, write an equation to represent the population after t years. 

What is ... P(t) = 15000 (1.05)t

100

The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number population of the town after 9 years.

What is... Approximately 42,640 people

100

Use y = 250(1.2)x What is the initial value?

What is... 250

100

Solve: 53-2x = 5-x

What is ... x = 3 

100

Simplify (6z-2)/(12z-1)

what is... (1)/(2z1)

200

A car depreciates at a rate of 12% per year. If the car's initial value is $18,000, write an equation for the car's value after t years. 

What is... V(t)=18000(0.88)t

200

$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?

What is... $1751.21

200

Use y = 250(1.2)x What is the growth factor?

What is... 1.2

200

Solve: 31-2x = 243

What is... x = -2

200

Re-write 645/6

What is...  x = 32 

300

The New York Mets sign a new player for $8,000,000 and his salary goes up by 3% every year. Write the function that models the amount of money the player makes as time goes on.

What is ... F(x) = $8,000,000(1.03)x

300

The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. What will the population of the town be in 5 years?

What is... Approximately 42, 499 People

300

Use y = 250(1.2)x What is the growth rate?

What is ... 20%

300

Solve: (1/5)-3x = 625

What is ... x = 4/3

300

Re-write 25(-3/2)

what is... 1/125

400

Using the ordered pairs: 

(0,150),(1,120)(2,96)(3,76.8)(4,61.44)(5,49.15)

What is ... P(x) = 150 (0.8)x

400

A car depreciates at a rate of 19% per year. After 8 years, the car is worth $4076.64. How much was the car worth when purchased? 

What is ... $22,000

400

y = 9.8(.35)x What is the decay factor?

What is... 0.35

400

Solve: 16x+3=643x+6

what is ...  x = -12/7

400

Simplify (100m17n13)/(5m12n19)

what is... (20m5)/(1n6)

500

You invest $2,000 in an account that compounds interest quarterly at a rate of 5%. Write an equation that represents the amount of money in the account after t years 

What is... A = 2,000(1 +(0.05/4))4t

500

A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present. When will the amount of the substance drop to below 20 grams (to the nearest year)? 

What is... Approximately 14 years 

500

y = 9.8(0.35)x What is the decay rate?

What is...  65%

500

Solve: 20-6x+6 = 55

What is... x = -1/3

500

Simplify (-x3y4)3(-5x2y)2

what is... -25x13y14