How do you find the domain and range of an exponential function?
1 answer:
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The answer to these two questions are not the same. We don't agree with Noah.
Reason:
Let's start with the first question.
1. Given: rate = 10% increase, base/original number = 550 bison
10% of 550 is:
10% of 550 is 55. Hence, there is an increase of 55 bison this year. This year, there are 550 + 55 = 605 bison in the herd.
2. Given: rate = 10% decrease, percentage/final number = 550 bison
Applying the concept of Percentage = Base x Rate, we can get the Base or the original number of bison before the decrease by dividing Percentage over Rate.
Filling in the formula with the given values in question 2, we have:
Last year, there were 611 bison.
As we can see, the answer for number 1 is 605 bison while the answer for the number 2 is 611 bison. The answer of the two questions are not the same.
Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
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<h3>Step 1</h3>Write the equation in standard form.
4x³ -16x² -84x = 0
<h3>Step 2</h3>Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
<h3>Step 3</h3>Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
<h3>Step 4</h3>Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
<h3>Step 5</h3>Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
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<em>Additional comment</em>
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
