MCR3U AOL 3 by catcookie

Question 2

lorraineyu — 2024-05-20 03:51:18 UTC

Simplify the following expression and express your answer with positive exponents.

Introduction 1

lorraineyu — 2024-05-20 04:08:25 UTC

About Integer Exponents:

Base is the number being multiplied, and exponent is how many times the base is being multiplied.
Any baseto the power of 0 is 1.
Integer base to the power of a negative exponent is equivalent to the reciprocal of the same base to the power of the opposite component.
Fractional base to the power of a negative exponent is equivalent to the reciprocal of the same base to the power of the possitive component.

Solution 2

lorraineyu — 2024-05-20 04:19:36 UTC

Steps to Solve:

Simplify the expression inside the parentheses using exponent laws for both the numerator and the denominator.
Combine the simplified expressions and further simplify.
Apply the outer exponent and simplify the resulting expression to positive exponents.

Introduction 2

lorraineyu — 2024-05-20 04:31:23 UTC

About exponents laws:

When mutiplying powers with the same base, add the exponens.
When diving powers with the same base, subtract the exponents.
When raising a power to a power, multiply the exponents.

About rational exponents:

A number to the power of a rational exponent is equivalent to a radical.

Question 1

lorraineyu — 2024-05-20 04:37:54 UTC

What is equal to 7/9 of negative 5?

Solution 1

lorraineyu — 2024-05-20 04:38:49 UTC

7/9 of negative 5 is equal to 9/7 of positive 5.

Introduction 3

lorraineyu — 2024-05-20 05:00:22 UTC

What is a exponential Function?

A function with a base (excluding 0 and 1) and a variable exponent.

Increasing exponential functions represent growth, |b| > 1.

Decreasing exponential functions represent decay, |b| < 1.

The domain of a exponential function is always {DER}, but the range of a exponential function is related to its hor. asymptote.

Question 3

lorraineyu — 2024-05-21 03:03:39 UTC

A certain type of plant has an initial height of 10 cm and grows according to the exponential function, where H(x) is the height in centimeters after xxx days.

Determine the height of the plant after 3 days.
Find the number of days xxx when the height of the plant reaches 160 cm.
Explain the domain and range of the exponential function.

Solution 3

lorraineyu — 2024-05-21 03:44:19 UTC

Introduction 4

lorraineyu — 2024-05-21 03:52:13 UTC

Given the usual formula of exponential function, we have to consider the different transformations, such as the value, sign of a, k and c, d. We haveto graph the base function and then apply the transformations.

Question 4

lorraineyu — 2024-05-21 04:07:53 UTC

Describe the transformations applied to f(x) to obtain g(x).
Determine the new y-intercept of the function g(x).

Solution 4

lorraineyu — 2024-05-21 04:16:33 UTC

Describe the transformations:

The term x+1 inside the exponent indicates a horizontal translation to the left by 1 unit.
The subtraction of 3 outside the exponent indicates a vertical translation down by 3 units.

So as a result, we should move the function 1 unit left and 3 units down.

Determine the new y-intercept:

If we setting x=0:

We can solve the function using the way in the picture.

So, the new y-intercept of the function g(x) is −1.

Introduction 5

lorraineyu — 2024-05-21 04:28:21 UTC

Given the formula equation, we have:

f(x)-final amount or number
a-initial amount or number
b-exponential growth or decay

If there is a growth, b=1+growth rate.

If there is a decay, b=1-decay rate.

Question 5

lorraineyu — 2024-05-21 04:31:47 UTC

A savings account has an initial balance of $1000 and grows at an annual rate of 5%. What will the balance be after 3 years?

Solution 5

lorraineyu — 2024-05-21 04:43:43 UTC

So, the balance after 3 years will be approximately $1157.63.