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harkovskaia [24]
2 years ago
11

Mark Brainliest and Give PoInts​

Mathematics
1 answer:
nata0808 [166]2 years ago
6 0

Answer: the 2nd and the 5th one

Step-by-step explanation:

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What best describes the asymptote of an exponential function of the form f(x)=b^x?
horrorfan [7]

It depends on the value of b


Exponential functions are defined for positive values of the base [ŧex] b [/tex]. Also, they're not defined if b=1, or at least let's say that this is a trivial case, since it is the constant function 1.


Case 0<b<1:

If the base sits between 0 and 1, the exponential function is constantly decreasing. The explanation is quite intuitive, assume for the sake of simpleness that b is rational. If it sits between 0 and 1, it means that it can be written as a fraction p/q, with p<q. So, if you give a large exponent to b, you obtain


\frac{p^x}{q^x},\quad p^x \ll q^x \text{ as } x \to \infty


On the other hand, if you consider negative exponents, you switch numerator and denominator and then raise to the same exponent the fraction q/p, which gets larger and larger.


So, if 0<b<1, we have


\lim_{x \to -\infty} b^x = \infty,\qquad \lim_{x \to \infty} b^x = 0


and thus 0 is a horizontal asymptote as x tends to (positive) infinity.


Case b>1:

This case is very similar, except all roles are inverted. Now you start with a fraction p/q where p>q. So, with positive, large exponents you get


\frac{p^x}{q^x},\quad p^x \gg q^x \text{ as } x \to \infty


And as before, negative exponents switch numerator and denominator, so the fraction becomes q/p and thus you have


\lim_{x \to -\infty} b^x = 0,\qquad \lim_{x \to \infty} b^x = \infty


So, again, 0 is a horizontal asymptote, but this time for x tending towards negative infinite.

6 0
3 years ago
Read 2 more answers
Determine if the given ordered pair is a solution to the equation. Show work full.
sleet_krkn [62]

Answer:

The ordered pair is not a solution of the equation

Step-by-step explanation:

we know that

If a ordered pair is a solution of a linear equation, then the ordered pair must satisfy the linear equation

we have

y=-3x-13

Substitute the value of x and the value of y of the given ordered pair in the linear equation and analyze the results

For x=-1, y=15

15=-3(-1)-13

15=3-13

15=-10 ----> is not true

so

the ordered pair not satisfy the equation

therefore

The ordered pair is not a solution of the equation

5 0
3 years ago
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of ​$28. Opti
irina [24]

Answer:

$9500

Step-by-step explanation:

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week= 19 X 40 = $760

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, 8x/100= 760

Or, 8x= 76000

Or, x= 76000/8= 9,500

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

8 0
3 years ago
Read 2 more answers
The size of an insect population doubles every week. If there are 25 insects initially present, how many insects will there be i
Nata [24]

Answer:

tence there will be 6,00 insects abter 8 weeks.

Step-by-step explanation:

8 0
2 years ago
A population has a mean of 40 and a standard deviation of 15. a sample of size 100 is taken at random from this population. the
krok68 [10]
Theirs alot of people in this world so watch out.

3 0
3 years ago
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