Properties of Logs
The expanded expression of log(y3)
What is 3 log(y)?
Evaluate f(4.2); f(x)=2x
What is 24.2= 18.38?
Solve for x;
ex= 8.75
What is x= ln(8.75)= 2.17?
Write the exponential equation:
The level of polution decreases exponentially. Initially the level is 4300. After 3 days, the level is 1100.
y=A0 eKt----> ln(0.25581)=K3---> -0.4544=K--->
A0=4300
(0, 4300)
(3, 1100)
What is y=4300e-0.4544t?
Select the function(s) that are exponential;
h(x)=10.6x
f(x)= 394+3x2
k(x)= x2-x+2
g(x)=2+3.1(10x+5)
What are h(x) and g(x)?
The condensed expression of [2 log(K)] + log(L)
What is log(K2L)?
Y- intercept of C(x)= 2 + 10x
What is C(0)= 2 + 10x= 2+100= 2+1= 3?
Solve for x;
19.8 - ln(x)= 11.7
What is x= e8.1= 3294?
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?
The 3 rules for expanding logarithms in math
What is
log(ab)= log(a)+log(b)
log(a/b)= log(a)-log(b)
log(ab)= b log(a)
The expanded expression of log((CD)/F)
What is log(C) + log(D) - log(F)?
Y-intercept for the function;
d(x)=2x-3
What is 20-3= 0.125
Solve for x;
80/(1+10-x)=70
What is x= 0.845?
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?
Solve for x
5.6+ex=1.1
What is no solution?
ex=-4.5
x=ln(-4.5)
no solution- cannot take log of a negative number
Condense the following:
ln(x)-4ln(x+1)
What is ln(x/(x+1)4)?
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
Solve for x;
-5+4 log(2x+1)=1
What is x= 10log(2x+1)= 105= 49,999.5?
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?
Which functions are increasing?
L(x)= 0.5(4x)
M(x)= 4.5x
N(x)= 5-x
P(x)= 3.8-x
Q(x)= 4.56x
R(x)=5-0.04x
What are L, M, and Q?
Rearrange, and solve for x:
ln(6ex)=2
What is x= 0.21?
Which function grows at a faster rate?
f(x)= 10x 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)= 3330g(x)= 10
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
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?
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