Exponent Rules
x5x2
x7
Square Root of 36
6
The common ratio is the number that is ______________
Multiplying
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. In the exponential function that represents its growth, what is the common ratio?
1.012
What is the difference between geometric and arithmetic sequences?
Geometric changes by multiplication. Arithmetic changes by addition/subtraction
x10 divided by x4
x6
Square Root 40
2 square root 10
Determines growth
Common Ratio > 1
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Write an equation to model its growth
f(x)=38300(1.012)x
What is the next number in the sequence?
2, 10, 50, _____
250
(2x)3
8x3
2 square root 27
6 square root 3
Determines decay
0 < common ratio < 1
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
Why does f(x)=3(2)x NOT represent the following sequence?
3, 6, 12, 24, ...
Correct formula is f(x)=3(2)x-1
(8x)0
1 (anything to the power of 0 is 1!)
7 square root 80
28 square root 5
What is the equation of an exponential function with a common ratio of 1/2 and initial value of 10
f(x)=10(1/2)x
The height of a bouncy ball can be represented by the function, h(x)=40(0.75)x
The initial height is ______. The ball is losing ____ percent of its height with every bounce.
40, 25%
Write a formula to represent the sequence below:
4, 12, 36, 108
f(x)=4(3)x-1
(2x4)3 divided by x12
8
Square root of x4
x2
In an exponential function, if f(0)=100, and f(2)=4, what is the equation?
f(x)=100(1/5)x
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
a) Write a formula to represent the sequence below:
20,000, 10,000, 5,000, 2,500, ...
b) What is the 14th term?
a) f(x)=20,000(1/2)x-1
b)2.44140625