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2 years ago

What type of function is represented by the table of values below

Mathematics

2 answers:

mezya [45]2 years ago

3 0

The difference in consecutive y values is increasing by double each time. 2^1, 2², 2³, 2⁴ etc so the function is exponential

Ira Lisetskai [31]2 years ago

3 0

<h2>Answer:</h2>

The function that is represented by the table of values is:

Option: B

B. exponential

<h2>Step-by-step explanation:</h2>

We are given a table of values as follows:

x y

1 2

2 4

3 8

4 16

5 32

Based on the table of values we see that the relation between the independent variable x and the dependent variable y is given by:

$y=2^x$

( since, when x=1 we have: $y=2^1=2$

when x=2 we have: $y=2^2=2\times 2=4$

when x=3 we have: $y=2^3=2\times 2\times 2=8$

and so on)

Hence, the relationship is exponential with base 2 and exponent x.

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Finding Derivatives Implicity In Exercise,Find dy/dx implicity.<br> xey - 10x + 3y = 0

uranmaximum [27]

Answer:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Step-by-step explanation:

Given:

The implicit equation is given as:

$xe^y-10x+3y=0$

In implicit differentiation, we treat 'y' as a function of 'x' and differentiate both sides of the equation with respect to 'x' and then collect all the $\frac{dy}{dx}$ together and finally solve for $\frac{dy}{dx}$ .

So, differentiating both sides of the above equation with respect to 'x'. This gives,

$\frac{d}{dx}(xe^y-10x+3y)=\frac{d}{dx}(0)\\\\\frac{d}{dx}(xe^y)+\frac{d}{dx}(-10x)+\frac{d}{dx}(3y)=0\\\\\textrm{Using product rule, (uv)' = uv' + vu'}\\\\(x\cdot e^y\cdot \frac{dy}{dx}+e^y\cdot 1)-10\cdot1+3\frac{dy}{dx}=0\\\\\frac{dy}{dx}(xe^y)+e^y-10+\frac{dy}{dx}(3)=0\\\\\textrm{Grouping}\ \frac{dy}{dx}\textrm{ terms together}\\\\\frac{dy}{dx}(xe^y+3)+e^y-10=0\\\\\frac{dy}{dx}(xe^y+3)=10-e^y\\\\\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Therefore, the derivative $\frac{dy}{dx}$ implicitly is:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

5 0

3 years ago

Trevor thinks that left-handed pitchers in a baseball league are more likely to strike out batters than right-handed pitchers ar

Scilla [17]

Answer:

C. H0: PL - PR = 0

Ha: PL - PR > 0

The null hypothesis for this case is that left-handed pitchers in a baseball league are not more likely to strike out batters than right-handed pitchers are. That is the proportion of at-bats resulting in a strikeout is significantly equal for both left-handed and right-handed pitchers.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

8 0

3 years ago

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

Salsk061 [2.6K]

Answer: In June 2097

Step-by-step explanation:

According to the model, to find how many years t should take for $P(t)=21100$ we must solve the equation $0.9t^2+6t+14000=21100$ . Substracting 21100 from both sides, this equation is equivalent to $0.9t^2+6t-7100=0$ .

Using the quadratic formula, the solutions are $t_1= \frac{-6-\sqrt{6^2 -4*0.9*(-7100)}}{2*0.9}=-92.21$ and $t_2=\frac{-6+\sqrt{6^2 -4*0.9*(-7100)}}{2*0.9}=85.54$ . The solution $t_1=-92.21$ can be neglected as the time t is a nonnegative number, therefore $t=t_2=85.54$ .

The value of t is approximately 85 and a half years and the initial time of this model is the January 1, 2012. Adding 85 years to the initial time gives the date January 2097, and finally adding the remaining half year (six months) we conclude that the date is June 2097.

6 0

3 years ago

Gabriel works at an amusement park. He loads 15 new passengers onto the roller coaster every 5/6 of a minute. At what rate does

dem82 [27]

Answer:

12 1/2 or 12.5

Step-by-step explanation:

all you have to do is multiply 15 times 5/6

4 0

3 years ago

Can someone please help.

zvonat [6]

Answer:

8 jars

Step-by-step explanation:

Let the number of jars is x.

<u>80 liters distributed, each jar has:</u>

80/x

<u>Redistribution with 4 less jars, each jar now has:</u>

80/(x - 4)

<u>Each jar has now twice the amount:</u>

80/x*2 = 80/(x - 4)
2/x = 1/(x - 4)
2(x - 4) = x
2x - 8 = x
x = 8

She prepared 8 jars at the start

4 0

3 years ago