Exponential Functions Review

Terminology

100

This type of function is represented by a graph that falls from left to right, passing through the points (0,1) and (1,b)

What is an exponential decay function?

200

The equation A=Pe^rt is used to model this hypothetical financial concept

What is continuously compounded interest?

300

The value 1.24 in the following function is called this: f(x)=850(1.24)^x

What is the growth factor?

400

This type of "magical" transformation has the power to change a growth function into a decay function

What is a horizontal reflection?

500

In an exponential growth model, f(x)=a(1+r)^t, the variable "r" represents this

What is the percent increase?

Transformations

100

This type of transformation can be found in the following function: f(x)= -4^x

What is a vertical reflection?

200

Identify each of the transformations that occur in the following function: f(x)= -1/2(6)^x

Vertical reflection & vertical shrink by a factor of 1/2

300

Construct an exponential function of base 3 that is reflected horizontally, vertically shrunk by a factor of 1/5, and translated 2 units down

f(x)= 1/5(3)^-x-2

400

Identify each of the transformations that occur in the following function: f(x)= -8(1/3)^-x-5+4

Vertical reflection, vertical stretch by a factor of 8, horizontal reflection, horizontal translation 5 units right, vertical translation 4 units up

500

Construct an exponential function of base 1/4 that is reflected vertically, reflected horizontally, vertically stretched by a factor of 5, translated horizontally 1 unit to the left, and translated vertically 7 units up

f(x)= -5(1/4)^-x+1+7

Compound Interest

100

This is the term for the initial amount of money that is put into an account

What is the principal?

200

In the compound interest formula, the percent increase is calculated by doing this operation

Dividing the annual interest rate by the number of times compounded per year

300

If a savings account has an annual interest rate of 1.25% that is compounded semiannually, find the growth factor of the account when it is expressed as an exponential equation

1.00625

400

You deposit $6000 in an account that pays 1.95% annual interest. Find the balance after 10 years when the interest is compounded quarterly.

$7288.41

500

Calculate the annual interest rate of the account modeled by the following equation:

A=4250(1.0043)^6t

2.58%

Exponential Equations

100

10^3x=10¹⁸

x=6

200

8^3x-6=1

x=2

300

16=4^-5x-18

x= -4

400

(1/5)¹²=(1/125)^x+6

x= -2

500

(1/216)^-3x+9=36^5x-14

x=1

Potpourri

100

The natural base that is approximately equal to 2.72

What is e?

200

When an account only earns interest on the initial principal that is deposited, it is known as this

What is simple interest?

300

6ln(3x)=54

2701.03

400

The exponential growth and decay "parent functions" have this asymptote in common:

y=0 (the x-axis)

500

Rewrite the following function in the form y=a(1+r)^t or y=a(1-r)^t:

y=a(4)^t/6

y=a(1+0.26)^t