Simplifying Exponents
Exponential Functions
All About Functions
Compound Interest
Potpourri
100
Use the exponent rules to simplify:
(x^3)^2 * x^1
x^7
100
Based on the table, determine the function rule:
f(x)=7*2^x
100
A tomato plant grows 3 inches per week. It starts at 6 inches tall.
Predict after 12 weeks the height of the tomato plant
42 inches
Linear Function Rule:
f(x)=3x+6
100
What is the compound interest formula?
100
After conducting a survey, a data set has a correlation coefficient number of
r=0.0358
Can the survey be trusted to be reliable? Why?
No because the correlational coefficient is closer to 0 than to 1 or -1
200
Use the exponent rules to simplify:
(3x^2 * 2x^2) / (2x^2)
3x^2
200
Use the function rule below to determine f(12)
f(x)=7*2^x
28,672
200
A bacteria begins with 2,500 cells and grows at three times it's size every month.
Determine how many cells the bacteria will have after 9 months of growth
49,207,500
Setup:
f(x)=2500*3^x
200
You invested your allowance of $270 which gets 15% compounded annually for 3 years.
How much will you have in 3 years?
$410.64
200
Type of correlation where x increases, y decreases.
Negative Correlation
300
Use the exponent rules to simplify:
(2xy^3 * 3xy)^2
Use the exponent rules to simplify:
36x^4y^8
300
Based on the table, determine the function rule:
f(x)=6*0.5^x
300
A candle is 30 cm tall and burns at a rate of 1.2 cm per hour.
Predict the height after 18 hours.
8.4 cm tall
Linear Function Rule:
f(x)=-1.2x+30
300
You invested $52,400 at 6% compounded annually for 5 years.
What is your total return on this investment?
$70,123.02
300
After conducting a survey, a data set has a correlation coefficient number of
r=-0.9837
Can the survey be trusted to be reliable?
Yes because the correlational coefficient is strong and closer to 1 than 0
400
Use the exponent rules to simplify:
(x^3y^4)^3*(3xy^2)^2
9x^11y^16
400
Use the function rule below to determine f(8)
f(x)=6*0.5^x
0.0234375
400
Say that Pierce City has a population of 1,500 people but is expected to decrease at a rate of 5% each year
Determine the approximate population of the town after 4 fours.
1,222 people
Setup:
f(x)=1500(1-0.05)^x
400
You borrowed $95 for 1 year at 5.2% interest that is compounded semi annually.
What will you pay back in full?
$100
400
Solve for x:
y=mx+b
x=((y-b))/m
500
Use the exponent rules to simplify:
(4b^2c^3 * 3bc^5) / (6b^3c^10)
2/c^2
500
When will an exponential function reach zero and cross the x-axis?
Never, unless the y-intercept is negative (ab^x-____)
500
Compare the two functions below and determine how they are different when graphed:
f(x)=2^-x
g(x)=-2^x
f(x) will start at 2 on the y-intercept and approach zero on the x-axis (BLACK LINE)
g(x) will start at -2 on the y-intercept and move away from zero on the x-axis (RED LINE)
500
Your investment of $18,100 at 13.6% compounded quarterly for 7.5 years will be worth how much?
$49,350.86
500
7 more than 3 times a number is the same as twice the difference of a number and 5.
What is that number?
-17
Setup:
3x+7=2(x-5)