Exponential Functions Algebra I Review

Exponential Functions

100

What is the general form of an exponential function?

f(x) = a b^x

200

What's the name of the line that a function gets closer and closer to but never crosses?

Asymptote

300

What is the domain and range of the following equation: y = -3 (4)^x ?

D: All real numbers

R: y < 0

400

What is the formula for an exponential function that fits the following set of points: (0, 1/2), (1, 2), (2, 8), (3, 32)?

y = (1/2) * 4^x

500

4 rats have found their way into my basement, and if unchecked they will double every year. If nothing is done about the rats, estimate how many years it will take for there to be 5000 rats in my basement.

Between 10-11 years

Exponential Growth

100

What is the formula for exponential decay?

A = P (1 - r)^t

200

Aren deposited $2000 into the bank, giving an 8% interest rate per year. Write an equation to represent the situation.

A = 2000 (1.08)^t

300

Morgan bought a car for $10,000, and it depreciates in value at a rate of 6% per year. How much will their car be worth after 5 years? Round to the nearest dollar. 

$7339

400

Gustav put $5000 into the bank under a plan where it will gain 9% interest compounded semi-annually. How much money will he have after 10 years?

$12058.57

500

Myrtle was given a fancy $5 spoon as a gift in 1920. Since vintage items tend to be given more worth when they are older, its worth grew at a rate of 36% every decade. How much would the spoon be worth in the year 2020?

$108.23

Geometric Sequences

100

Is the following sequence arithmetic, geometric, or neither?

1, 3, 6, 10...

Neither

200

Write the recursive formula for the geometric sequence 1, 3, 9, 27, 81...

a₁ = 1; a_n = 3 * a_n-1

300

Write the explicit formula for the function based on the following recursive formula:

a₁ = 7;   a_n = (1/3) a_n-1

a_n = 7 * (1/3)^n-1

400

Find the 12th term of the sequence (7/3), 7, 21, 63...

a₁₂ = 413343

500

If a₁ = 48 and a₅ = 3 are the 1^st and 5th terms in a geometric sequence, what are the first 5 terms in the sequence?

48, 24, 12, 6, 3

Transformations

100

In what direction is the graph of y = 2^x shifted to match y = 2^x + h, when h > 0?

Up

200

Describe the transformation from f(x) = (1/2)^x to g(x) = (1/2)^x-3

Shift right 3

300

What is the domain and range of the following equation: y = (1/3)^x + 7?

D: All Real Numbers

R: y > 7

400

f(x) = 3^x-2 + 1

g(x) = 3^x-2 - 9

Describe the transformation from f(x) to g(x).

Shift 10 units down

500

If f(x) = 2^x, and g(x) is the result of shifting f(x) left 4 units, evaluate g(1).

g(1) = 32

Exponent Rules

100

What is x * x²?

x³

200

Simplify the equation on the board. Write as a fraction if necessary.

w²

300

Simplify (2x³ )²

4x⁶

400

Simplify the equation on the board. Write as a fraction if necessary.

2y²

500

If x^1/2 * x^1/2 = 9, what is x^1/2 equal to?

x^1/2 = 3