Simplify x18/x6
x12
y=a(b)x, what does "a" and "b" represent?
a is the y-intercept (starting value) and constant multiplier (rate)?
Create an exponential function that might have the following graph
y=a(b)x
a: positive #
b: positive # larger than 1.
x: variable
A savings account earns 4% interest per year. If Josiah puts 500 dollars in now, What's the equation to find out how much will he have after 5 years?
y=500(1.04)5
Given $1000 compounded quarterly at an annual 12% interest rate. What is the quarterly interest rate?
3%
Simplify (28n9)0
1
Given the function f(x) = 10(5)x, evaluate f(3).
1250
Describe a series of transformation to the graph of f(x)=2(3)x to obtain the graph of g(x)=2(3)x+1-4
f(x) translate 1 units right and 4 units down to obtain g(x)
The population of a small town is decreasing at a rate of 2% per year. in 1970 the population was 25,000. This is what the approximate population would be in the year 2020.
9104
Given $1000 compounded quarterly at an annual 12% interest rate. What is the equation for this?
y=1000(1.03)4t
Simplify -5a2/3x-3 without negative exponent
(-5 3√a2)/x3
What's the equation for these points: (-1, .5),(0,3),(1,18),(2,108) ?
y=3(6)x
What is the period, frequency, and amplitude of the sinusoidal function: y=-13cos(3πx)
period: 2/3;
frequency: 3π
amplitude: 13
The number of students in the book club is increasing at a rate of 15% per year and they started with 9 students. How much would they have after 7 years?
What is ~24 students?
Given f(x)=5000(1.015)4x What is the interest rate?
6% annually interest; or
1.5% quarterly interest
Simplify (-3x4y3z1/2)4
81x16y12z2
Write the inverse function of the exponential function y=5x.
y=log5 x
Describe the difference of the graphs of these two functions: f(x)=4(1/2)x and g(x)=4(1.8)x
f(x) is decay, or as x increases, y decreases
g(x) is growth, as x increases, y increases
Fluorine-20 has a half-life of 11 seconds. This is the amount of fluorine-20 left from a 50 gram sample after 44 seconds.
3.125 grams
Describe a series of transformation of y=sinx to become a new function y=2sin(x-4π)+3
translate 4π units to the right, amplitude multiply by 2 which is vertical stretch by a factor of 2, and translate 3 units up.
Using the Pythagorean identity if cosA=0.6, and A is in Quadrant IV. Find the value of sinA. and the value of tanA.
sinA=-0.8; tanA=-4/3
)The graph of an exponential function, V, passes through the points (0, 2) and (3, 128) as shown on the graph below. Write an equation for the function V(x).
What is V(x)=2(4)x
Find the equation that models the following table.
y=3(2)x
Beth and Bill are playing a game with 8 sided dice. A die has 2 blue sides, 2 red sides, 2 orange sides, and 2 green sides. They start with 200 dice and roll them. If an orange side comes up, they remove those dice and roll the remaining dice again. Write an equation to model Beth and Bill’s game.
y = 200(2/8)x
If sin2(32o)+cos2(x)=1. What is the value of x?
32o