Exponential Functions

Standard Form

100

Consider the function f(x)= 3^x. Name the a and b value of the function.

a=1 and b=3

200

f(x) = 500(0.85)^x. Name the a and b value of the function.

a=500 and b=0.85

300

f(x)=12(1.13)^x. By what percentage is this function increasing?

13%

400

f(x) = 500(0.85)^x. Find f(6.5). Round to the nearest hundredths.

173.86

500

f(x) = 500(0.85)^x. Estimate the value of x when f(x)=222.

x=5

Vertical Shifts

100

Write an equation for an exponential function with a=2, b=12, and k=3

f(x) = 2(12)² + 3

200

Write an equation for an exponential function with a=1/2, b=2/3, and k=-7

f(x)=1/2 (2/3)^x - 7

300

Give an exponential equation where a=4000, b=2, and k=10. At what value for y is the horizontal asymptote located?

y=4010

400

Give an exponential equation where a=200, b=1/3, and k=-15. At what value for y is the horizontal asymptote located?

y=185

500

Write an equation with a horizontal shift. Identify the a value, b value, and k value. Write an equation for the horizontal asymptote. 

Answers vary. 

Writing Equations

100

There are 20 birds at the sanctuary. The population grows at a rate of 23% per year. Write an equation.

f(x)=20(1.23)^x

200

Ryan bought a brand new car for $18,000. Its value depreciated at a rate of 1.2%. Write a function to represent the value of the car over time. 

f(x)=18000(0.988)^x

300

Ms. Gerety borrows $40,000 from the bank to fix the siding on her home. The bank charges her an annual interest rate of 7.9%. Write an equation to show how much Ms. Gerety owe each year.

f(x)=40,000(1.079)^x

400

In 2012, the pop. of a city was 63,000. By 2017, the pop. was 54,100. Find the b-value.

b=0.97

500

Ainsley works at a bookstore. Her starting salary is $24,500, and she gets a 3% raise each year. How many years until she makes approximately $35,000. 

12 years

Rewind

100

What is the domain and range of a linear function?

All real numbers

200

What is the Pythagorean Theorem? Draw a triangle and identify each side. 

a²+b²=c²

300

What is the equation for a line in point-slope form?

y-y₁=m(x-x₁)

400

Write 5^(2/3) as a radical.

cubed root of 5 squared

500

What is Ms. Gerety's favorite ice cream flavor?

Mint Chocolate Chip

Growth or Decay

100

j(x) = 4(1/4)^x

Determine the growth or decay factor

decay factor of 75%.

200

h(x)=2(5)^x

Determine the growth or decay factor

growth factor of 400%

300

f(x) = 6(1.05)^x

Determine the growth or decay factor

Growth factor of 5%

400

p(x) = 2(1.34)^x

Determine the growth or decay factor

Growth factor of 34%

500

g(x)=500

remains constant. No growth or decay.