Misc.
Graphing
Log Properties
Log/Exponential Equations
Word Problems
100
Does this equation's graph show growth or decay?
f(x)=1/3(2x)-1
growth (2 is base)
100
What would be the transformation of 3x+1
Vertical shift up 1
100
Convert this to logarithmic form: 45=1024
What is log 4 1024 = 5
100
4x=64
What is 3?
100
the amount Rico must pay back if $25,000 is borrowed at 12% for 6 years if it's compounded monthly
What is $51,177.48?
200
An exponential equation contains the points (0,.25) and (4,4). What could the equation be if it were in the form:
ab^x
(1/4)(2^x)
200
What is the x-intercept of all non translated exponential graphs
does not exist.
200
Solve for x using the properties of logarithms:
log26-log23=x
x=1
200
log 6 (x/2 - 4)= log 6 25
What is 58?
200
Create an equation using the following information:
The attendance at JHMR increases by 8% on a yearly basis. If the average amount of daily users for 2020 was 4500, setup an equation that might calculate the average daily users in the future according to x (years past 2020)
f(x) = 4500(1.08)^x
300
Find the inverse of this equation: f(x)=log3(2x+4)
f-1(x)=(3x/2)-2
300
True or False, the line y=-2 is an asymptote for the graph of
f(x) = 10^(x-2)
Justify your answer.
False.
300
Fill in the blank with a log statement, base 3:
_________= 2
What is 2 = log 3 9
300
log x + log (x + 4) = log 12
What is 2?
300
If Bill has $2 that gets compounded by 70% monthly, how long will it take to have $3,000,000?
About 20.9 years
400
Solve for x:
ln(-3)=x
*no calculators allowed. perhaps graph?*
Undefined.
400
What transformations are applied to the following function:
-b^(-x)+2
- reflection over y and x axis
- vertical shift up 2
400
True or False:
log2x - log2y=log2(x/y)
True
400
log 5 - log (2x - 1) = 1
What is 3/4?
400
Create an equation using the following information:
After signing up for a fad diet that Gweneth Paltrow started, you see that the weight is just FALLING off. You used to be 140lbs but since starting the diet, you lost 2.5% of your body weight per week.
f(x) = 140(.975)^x
500
Which equation represents this graph?
a. f(x)=log4(x)-6
b. f(x)=log3(x+3)-5
c. f(x)=log(2)
d. f(x)=ln(x+15)
b. f(x)=log3(x+3)-5
500
Find the Domain, Range, x-intercept, and vertical asymptote of the logarithmic function and draw a sketch of:
g(x) = ln(-x)
domain: (-inf, 0)
range: (-inf, +inf)
x-intercept: (-1,0)
vertical asymptote: x=0
500
log(x) - 2log(y) + 3log(z). condense to a single quantity.
log(xz3)/log(y2)
500
log 5 x + log 5 (x + 24) = 2
What is 1?
500
The population of a bacteria is 50,000 and increases by a growth rate of 85% per hour. How long will it take the population to double (days to nearest hundredth)?
29.76 days