Unit 6 - Exponential Functions
rate
% that an amount is changing by
(-15r⁶s⁷t⁴)/(3r²s⁹t⁷)
(-5r⁴)/(s²t³)
(9a²bc⁴)/(15ab³c⁵)
(3a)/(5b²c)
product rule
(x³)(x⁵)=x³⁺⁵
power rule
(x³)⁵=x¹⁵
(-4x²)/(24x⁵)
-1/(6x³)
(-2x²y)²(-3xy³)
-12x⁵y⁵
3a³b²-5a³b²
-2a³b²
5xy-2x²y+2xy
-2x²y+7xy
(3x)⁻³
1/(27x³)
Exponential Function
A function with the general form f(x) = a * b^x + k
Exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself, used as an input value for an exponential function.
Constant
A non-variable value that determines vertical shift and is added or subtracted to an exponential function.
4308
A population of fish starts at 8000 and decreases by 6% each year. What is the population after 10 years?
Compression
A result of a coefficient that is between 0 and 1, pushing an exponential function towards from the x-axis.
Stretch
A result of a coefficient that is greater than 1, pulling an exponential function away from the x-axis.
Vertical Shift
A result of a constant being added to a exponential function, moving an exponential function up or down.
Exponential Decay
A result of an exponential function having a base value that is between zero and one, decreasing from left to right.
Exponential Growth
A result of an exponential function having a base value that is greater than one, increasing from left to right.
Coefficient
A value multiplied with the base value, causing stretch or compression.
Base
A value that determines exponential growth or decay, it is always attached to exponent
Parent Function
An exponential function containing just the base and exponent.
855,355.66
Annual Sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% each year. What are the annual sales after 7 years?
23,219.72
Daniel's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. What is the approximate value after 8 years?
135
During a certain period of time, about 70 northern sea otters had an annual growth of 18%. How many otters would there be after 4 years?
decreases
Exponential Decay
depreciates
Exponential Decay
The population (y) halves
Exponential Decay Decay factor of 1/2
appreciates
Exponential Growth
growing
Exponential Growth
increases
Exponential Growth
The population (y) doubles
Exponential Growth Growth Factor of 2
the amount (y) Triples
Exponential Growth Growth Factor of 3
zero exponent rule
x⁰=1
quotient rule
x⁵/x³=x⁵⁻²
negative exponent rule
x⁻¹=1/x
Exponential Decay Function
y=a(1 - r) ^x
Exponential Growth Function
y=a(1+r)^x
exponential function
y=starting value(rate)^x y = a*b^x
14,310.91
Kathy plans to purchase a car that depreciates at a rate of 12% per year. The initial value of the car is $21,000. What is the value of the car after 3 years?
Changing a % into a decimal
Move decimal two spaces left
y-intercept
The coordinate at which a graph intersects the y-axis.
956
The population of a school is 800 students and is increasing at a rate of 2% per year. What is the population after 9 years?
2092
The population of a town is 2500 and is decreasing at a rate of 3.5% each year. What is the population of the town after 5 years?
424,527.63
Twenty years ago, Mr. Davis purchased a home for $160,000. Since then, the value of the home has increased by about 5% per year. What is the value of the home today?
Linear Function
a function in which the graph of the solutions forms a line
(a⁴)(a³)
a⁷
Compound Interest
interest calculated on both the principal and the accrued interest
growth or decay factor
the fixed multiplier
Exponent
the power to which a number, symbol, or expression is to be raised
initial value
the starting amount or y-intercept of the graph