Unit 3 Assignment by

Integer Exponents:

yunmenggu2025 — 2024-05-18 22:26:33 UTC

An integer exponent represents an integer power of a number.
When the exponent is positive, it represents repeated multiplication of the base.
When the exponent is a negative, it means that the reciprocal of the base number is a positive exponent.

Rational Exponents:

yunmenggu2025 — 2024-05-18 22:28:22 UTC

Rational exponents are exponents expressed as fractions.
They represent roots or fractional powers of a number.

Exponent Laws:

yunmenggu2025 — 2024-05-18 22:31:01 UTC

The law of exponents is the behavior of exponents in multiplication, division, and exponentation operations.
The key laws include the product of powers, power of a power, power of a product, and quotient of powers.

Question 1

yunmenggu2025 — 2024-05-18 22:39:03 UTC

Solution 1

yunmenggu2025 — 2024-05-18 22:42:11 UTC

Apply the exponent laws

yunmenggu2025 — 2024-05-19 00:53:31 UTC

Question 2

yunmenggu2025 — 2024-05-19 00:56:10 UTC

Solution 2

yunmenggu2025 — 2024-05-19 00:56:56 UTC

Growth and decay

yunmenggu2025 — 2024-05-19 00:59:26 UTC

Exponential growth: A function whose variable is exponential and whose base is greater than 1. They have shown quick growth over time.

Exponential decay: A function in which the variable is in an exponent and the base is between 0 and 1. Over time, they decay quickly.

Domain and range: The domain of an exponential function is real, and the range depends on whether it grows or decays.

Transformations

yunmenggu2025 — 2024-05-19 01:01:05 UTC

Horizontal stretching and compression: Affects the width of the graph by looking at the value of k

Vertical stretching and compression: Affects the height of the graph by looking at the value of a

Y-axis reflection: Reflection in the Y-axis.

X-axis reflection: Reflection in the X-axis.

Horizontal Translation: Moves the graph to the left or right.

Vertical Translation: Moves the graph up or down.

Question 3

yunmenggu2025 — 2024-05-19 01:09:39 UTC

Solution 3

yunmenggu2025 — 2024-05-19 01:10:14 UTC

Question 4

yunmenggu2025 — 2024-05-19 01:16:53 UTC

Solution 4

yunmenggu2025 — 2024-05-19 01:17:17 UTC

Question 5

yunmenggu2025 — 2024-05-19 01:23:18 UTC

Solution 5

yunmenggu2025 — 2024-05-19 01:24:11 UTC

Apply

yunmenggu2025 — 2024-05-19 01:43:21 UTC

f(x)-final number

a-initial number

b-exponential growth or decay

if there is growth，b=1+growth rate
if there is decay，b=1-decay rate

x-number of growth or decay periods

Important point

yunmenggu2025 — 2024-05-19 01:44:48 UTC

Make sure the units are consistent