Exponent Properties
Simplify the expression:
43 * 42
43 +2 = 45
Is this function an exponential growth or decay?
y = 4(1.65)t
Growth
A rational exponent is an exponent that is a fraction...
yes or no
yes
The curve of an exponential growth graph is ___________, while the curve of an exponential decay graph is _______________.
increasing
decreasing
False
y = a(1+r)t
Simplify the expression:
[(-4)3]2
-43 * 2 = -46
What is the percent rate of change in this function?
y = 10(0.05)t
.95 = 95%
a1/n, the denominator n is the ___________
index
Which of the following does not represent an exponential function?
a. y =(0.25)x
b. y =4* (3/2)x
c. y= 2x+4
d. y= (0.5)x +2
c. y = 2x+4
The formula for exponential decay is y = a(1-r)t.
True
Simplify the expression
(k3)-2
k3 * -2 = k-6
= 1/k6
The house is worth 9,000 dollars and the price increases by 20%. Write a function that represents the value of house after t years.
y = 9,000( 1+.2)t
Evaluate the expression.
1003/2
1000
Tell whether the table represents an exponential function. Why?
x: -1 | 0 | 1 | 2
y: 2 | 8 | 32 | 128
Yes because the y is being multiplied by 4.
When there is no number shown in the index, that means that it's always 1.
False.
It is always 2 (square root)
Simplify the expression:
(4r3/2r5)
(4r3/2r5)
= 2r-2
= 2/r2
You buy a used car for $6599. Its value decreases by 12% every year.
(a) write the function that represents the value y of the car after t years.
(b) What is the value of the car after 2.5 years?
(a) y = 6599(1 - .12)t
(b) y = 6599(1 - .12)2.5
= $4794
Rewrite the expression in exponent form and evaluate.
(radical 9)3
93/2
= 27
Graph the function:
y = 4 * (0.5)x
Answer shown on the board...
Graph should be decreasing towards the right with the y-intercept at 4, (0,4).
You can tell when a table represents an exponential function when the y's add up by a number.
False.
You can tell when the y's multiply by a number.
Simplify the expression.
(5x0/ 10x-3y2)2
(5x0/ 10x-3y2)2
= 1x6/ 4y4
You deposit $2000 in an account that pays 4% annual interest. Find the balance after 8 years if the interest is compounded semi-annually.
2000( 1 + .04/2)2*8
= $2745.57
Evaluate the expression.
12-1/2 * 125/2
= 12(-1/2) + (5/2)
= 12 4/2
= 122
= 144
Without graphing, explain how the graph of the given functions are related to the graph f(x)= (0.5)x.
n(x)= -4 (0.5)x
The graphs are the same, but the only difference is that the second graph has a y-intercept of -4. Therefore this graph passes through the y axis at (0,-4).
In a compound interest problem, the n is determined by the number of times interest is compounded per year.
True