Algebra and Trigonometry Review Jeopardy

Properties of Logs

100

The expanded expression of log(y³)

What is 3 log(y)?

200

The condensed expression of [2 log(K)] + log(L)

What is log(K²L)?

300

The expanded expression of log((CD)/F)

What is log(C) + log(D) - log(F)?

400

Condense the following:

ln(x)-4ln(x+1)

What is ln(x/(x+1)⁴)?

500

Rearrange, and solve for x:

ln(6e^x)=2

What is x= 0.21?

Exponential Functions

100

Evaluate f(4.2); f(x)=2^x

What is 2^4.2= 18.38? 

200

Y- intercept of C(x)= 2 + 10^x

What is C(0)= 2 + 10^x= 2+10⁰= 2+1= 3?

300

Y-intercept for the function;

d(x)=2^x-3

What is 2^0-3= 0.125

400

The average rate of change of the function g(x)=10x+8 between x=1 and x=4

What is (48-18/4-1)= 10

500

Which function grows at a faster rate?

f(x)= 10^x between x=1 and x=4

g(x)= 10x + 8 between x=1 and x=4

What is f(x)?

average rate of change:

f(x)=(10,000-10/4-1)= 3330

g(x)= 10

Ex... and Log Equations

100

Solve for x;

 e^x= 8.75

What is x= ln(8.75)= 2.17?

200

Solve for x;

19.8 - ln(x)= 11.7

What is x= e^8.1= 3294?

300

Solve for x;

80/(1+10^-x)=70

What is x= 0.845?

400

Solve for x;

-5+4 log(2x+1)=1

What is x= 10^log(2x+1)= 10⁵= 49,999.5?

500

The probability that a genetic mutation becomes fixed is p. It depends on the selective advantages (s), and the number of breeding individuals (N). (Kimura and Ohta 1969).

p=(1-e^-2s)/(1-e^-4Ns)

If we want the probability at 0.3 (30% chance), and the selective breeding advantage is 0.2, how many individuals should there be?

What is 2?

0.3(1-e^-0.08N)= 1-e^-0.04

1-e^-0.08N = (1/0.3)(1-e^-0.04)= 0.1307

e^-0.08N= 0.8693

-0.08N=ln(0.8693)

N=(1/-0.08) ln(0.8693)= 1.75 = 2

Exponential Models

100

Write the exponential equation:

The level of polution decreases exponentially. Initially the level is 4300. After 3 days, the level is 1100.

y=A₀ e^Kt----> ln(0.25581)=K3---> -0.4544=K--->

A₀=4300

(0, 4300)

(3, 1100)

What is y=4300e^-0.4544t?

200

The decline of the pollution occurs exponentially. Initially the level is 4300. After 3 days, the level is 1100.

What will the level be after 9 days?

What is 72?

300

The decline of the pollution occurs exponentially. Initially the level is 4300. After 3 days, the level is 1100.

When will the level be 5?

What is after 14.9 days?

400

A logistic model has the form f(x)=c/1+ae^-bx

a, b, and c are positive constants

Initial value of this model, f(0)?

What is C?

500

A logistic model has the form f(x)=c/1+ae^-bx

a=1.3, b= -0.12, and c= 60 are positive constants

The carrying capacity? (The value as f(x) as x gets very, very large)

What is 60?

Random

100

Select the function(s) that are exponential;

h(x)=10.6^x

f(x)= 39⁴+3x²

k(x)= x²-x+2

g(x)=2+3.1(10^x+5)

What are h(x) and g(x)?

200

The 3 rules for expanding logarithms in math

What is

log(ab)= log(a)+log(b)

log(a/b)= log(a)-log(b)

log(a^b)= b log(a)

300

Solve for x

5.6+e^x=1.1

What is no solution?

e^x=-4.5

x=ln(-4.5)

no solution- cannot take log of a negative number

400

Which functions are increasing?

L(x)= 0.5(4^x)

M(x)= 4.5^x

N(x)= 5^-x

P(x)= 3.8^-x

Q(x)= 4.5^6x

R(x)=5^-0.04x

What are L, M, and Q?

500

Solve for x

ln(x)+ln(3x)=4

What is 4.27?

ln(x*3x)=4

ln(3x²)=4

3x²= e⁴

x²= e⁴/3

x= (e⁴/3)^1/2