Algebra 2 Review Game

Linear, Quadratic, Exponential models

100

A study of the red tailed hawk population in a given area shows the population, H(t), can be represented by the function H(t)=50(1.19)^t where t represents the number of years since the study began. In terms of the monthly rate of growth, the population can be best approximated by the function

a. H(t)=50(1.015)^12t      c. H(t)=50(1.19)^12t

b. H(t)=50(1.15)^t/12       d. H(t)=50(1.19)^t/12

a. H(t)=50(1.015)^12t 

200

The growth of a %500 investment can be modeled by the function P(t)=500(1.03)^t , where t represents time is years. In terms of the monthly rate of growth, the value of the investment can be best approximated by

a. P(t)=500(1.00247)^12t     c. P(t)=500(1.03)^12t

b. P(t)=500(1.00247)^t        d. P(t)=500(1.03)^t/12

a. P(t)=500(1.00247)^12t

300

Luminescence is the emission of light that is not caused by heat. A luminescent substance decays according to the function below. 

                       I = I₀e^3(-t/0.6)

The function can be best approximated by 

a. I=I₀e^(-t/0.18)      c. I=I₀(0.0067)^t

b. I=I₀e^5t             d. I=I₀(0.0497)^0.6t

 c. I=I₀(0.0067)^t

Set notation, Independence

100

Given y= -2x and x² + y² = 5, the point of intersection in quadrant II is 

a. (1, -2)          c. (-1, 1)

b. (-2,1)           d. (-1, 2)

d. (-1, 2)

200

At the Lakeside Resort, the probability that a guest room has a view of the lake is 0.24. The probability that a guest room has a queen-size bed is 0.74. Let A be the event that the guest room has a view of the lake, and let B be the event that the queen-size bed. Events A and B are found to be independent of each other.

Determine the exact probability that a randomly selected guest room has a view of the lake and a queen-size bed. 

P(Q and V)=P(Q) x P(V)

P(Q and V)=(.74)(.24)

P(Q and V)=.1776

Answer: .1776

300

Given that i is the imaginary unit, the expression (x-2i) is equivalent to

a. x²+4           c. x²-2xi-4

b. x²-4            d. x²-4xi-4

 d. x²-4xi-4

Transformations, inverses, sequences/series

100

An initial investment of $5000 in an account earns 3.5% annual interest. Which function correctly represents a recursive model of the investment after n  years. 

a. A=5000(0.035)ⁿ          c.  A=5000(1.035)ⁿ

b. a₀=5000                    d. a₀=5000 

    a_n = a_n-1(0.035)             a_n=a_n-1(1.035)

d. a₀=5000

    a_n=a_n-1(1.035)

200

If f(x)=1/2x³+3x-4x and g(x)=5log₃(x+10), then which value, rounded to the nearest tenth, is not a solution to f(x)=g(x)?

a. -6.9         c.2.2

b.-1.4          d. 9.8

b.-1.4    

300

Consider the recursively defined sequence below. 

                         a₁=8

                         a_n=2a_n-1

which explicit formula represents the same sequence?

    a. a_n=2ⁿ                  c. a_n=2ⁿ⁺²

    b. a_n=2(4ⁿ)             d. a_n=8ⁿ

c. a_n=2ⁿ⁺²