PROPERTIES OF EXPONENTS
When you multiply two like bases, you do "this" to the exponents.
What is ADD.
Write as a radical 41/4
4th root of 4
The function y = abx determines "this".
What is an EXPONENTIAL FUNCTION.
Label the following function: f(x) = a(1 - r)x
Exponential decay function
Doing "this" will help you solve exponential equations with unlike bases.
What is REWRITE EACH SIDE OF THE EQUATION USING THE SAME BASE, THEN SET THE EXPONENTS EQUAL TO EACH OTHER AND SOLVE.
When you divide two like bases, you do "this" to the exponents.
What is SUBTRACT.
Write the radical using a rational exponent.
(3x)2/5
Evaluating y = -7(2)x when x = -5 will give you "this" result.
What is -7/32.
Identify the initial amount a and the rate of growth r (as a percent) of the exponential function. Evaluate the function when x = 5. Round your answer to the nearest tenth.
y = 50(1 + 0.25)x
What is a = 50, r = 25%, and y = 152.6.
Solve the equation: 45x = 410
What is x = 2.
Any base raised to the zero power will give you a unique result.
What is ONE.
Determine if the following sequence is geometric. If it is what is the common ratio?
9, 3, 1, 1/3, 1/9, ...
Yes, r = 1/3
y = 5x + 3 represents an exponential function.
False, it is a linear function.
Write a function that represents the following situation: Profits of $100,000 increase by 15% each year.
What is f(x) = 100,000(1.15)x.
Solve the equation: 7x - 5 = 49x
What is x = -5.
How to make a negative exponent located in the denominator positive.
What is BRINGING THE BASE/EXPONENT UP TO THE NUMERATOR.
Determine if the following sequence is geometric. If it is what is the common ratio?
1, 1, 2, 3, 5, ...
No
Evaluating f(x) = 1/9(27)x when x = 2/3 will give you "this" result.
What is 1.
A school population of 1200 decreases by 6% each year, write the simplified exponential function
What is y = 1200(.94)x
Solve the equation: (1/5)x = 125
What is x = -3.
When there is an exponent located inside the grouping symbol raised to another exponent, you do "this" to the exponent.
What is MULTIPLY.
Write the recursive and explicit formula for this geometric sequence.
18, 54, 162, 486, 1,458, ...
an=18(3)n-1
an=3(an-1)
The function y = 3(2)x represents the population of bees in a beehive where x represents the number of days. How many bees are in the beehive after 4 days?
What are 48 BEES.
Determine whether the following represents an exponential growth function, an exponential decay function, or neither.
x = 0, 1, 2, 3; y = 4, 12, 36, 108
EXPONENTIAL GROWTH FUNCTION
Solve the equation: 36-3x+3 = (1/216)x+1
What is x = 3.