OLD STUFF
Log/Exp Functions
Simplifying Logarithms
Log/Exp Equations
Exp Applications
100
Find
tan((13π)/6)
sqrt(3)/3
100
For the function 2^(x-1)+5
Determine:
a) Domain
b) Range
c) y-intercept
d) Asymptote
Domain: (-∞,∞)
Range: (5,∞)
y-intercept: (0,5.5)
Horizontal Asymptote: y=5
100
log_9(1/3)
-1/2
100
3^(3x-1)=243
x=2
100
John deposited $3,500 in an investment account that earns 2.6% annual interest. If he makes no other deposits or withdrawals, find the total amount in the account after 6 years if it is compounded monthly.
$4090.20
200
Solve for 0≤x<2π:
sin(x)=-sqrt2/2
(5π)/4 and (7π)/4
200
What is the domain of a logarithmic function? Why?
Domain: (0,∞)
Raising a positive number to a power is never negative
200
lnsqrt(1/e^3)
-3/2
200
log(-4x+7)=log(-x)+log(6)
x=-7/2
200
How long will it take an investment earning 4.3% interest, compounded quarterly, to double?
16.2 years
300
Graph the following function:
f(x)=4cos(x)-1
300
BONUS ROUND:
What was the final score of the Superbowl LIX?
40-22
300
3log_2(4^(-5x))
-30x
300
32^(2x-1)=(1/16)^(-2x)
x=5/2
300
$3,000 was invested for 8 years with the interest compounded continuously. If the investment is worth $7,700 at the end of 8 years, what was the interest rate?
11.78%
400
Find an equation for the function below
f(x)=2cos(1/2x)+2
400
For the function log_2(x+4)-1
Determine:
a) Domain
b) Range
c) y-intercept
d) Asymptote
Domain: (-4,∞)
Range: (-∞,∞)
y-intercept: (0, 1)
Vertical Asymptote: x=-4
400
log_(3sqrt(n))(n^(3/4))
9/4
400
log_7(x+1)+log_7(x-5)=1
x=6
400
A colony of bacteria doubles every 6 hours. How long does it take the colony to triple in size?
9.51 hours
500
Solve for 0≤x<2π:
2cos^2(x)-cos(x)-1=0
x=0, (2π)/3, (4π)/3
500
In an exponential function y=a*b^x what values of b make a graph that illustrates exponential decay?
0<b<1
500
Given log_bK=-0.6, log_bJ=-5.2, log_bL=7.3 determine the exact value of log_b((KL^2)/(Jb^3))
16.2
500
ln(x+8)-ln(x-4)=10
x=(8+4e^10)/(e^10-1)=(-4(e^10+2))/(1-e^10)
500
The half-life of Plutonium 241 is 14 years. Thelma discovered a sample of plutonium 241 in her lab’s storage facility showing that it was put into storage 20 years ago. The sample currently weighs 55 grams. What did the sample weigh when it was put into storage?
148 .05g