Given the universal set U

Find the formula for an exponential function that passes through the two points give.

Ksenya-84 [330]

Answer:

$y=3(2)^{x}$

Step-by-step explanation:

Given.

Two points are given.

$(x, y)=(-1,\frac{3}{2})$ and $(x, y)=(3,24)$

An exponential function is in the general form.

$y=a(b)^{x}$ -------(1)

We know the points $(-1,\frac{3}{2})$ and $(3,24)$

put the first point value in equation 1

$\frac{3}{2}=a(b)^{-1}$

$\frac{3}{2}=\frac{a}{b}$

$a=\frac{3}{2}\times b$ --------(2)

put the second point value in equation 1

$24=a(b)^{3}$ ----------(3)

Put the a value from equation 2 to equation 3

$24=\frac{3}{2}\times b(b)^{3}$

$b^{3+1}=\frac{24\times 2}{3}$

$b^{4} = 16\\b=\sqrt[4]{16} \\b=2$

Put the b value in equation 2

$a=\frac{3}{2}\times 2$

$a=3$

Put the a and b value in equation 1

$y=3(2)^{x}$

So, the exponential function that passes through the points $(-1,\frac{3}{2})$ and $(3,24))$ are $y=3(2)^{x}$ .

6 0

2 years ago

Consider the sequence 1, –3, 9, –27, 81, … Which statement describes the sequence?

ludmilkaskok [199]

Answer:

There is a similar problem with the same numbers except with no negatives so it goes 1 , 3 , 9 , 27, 81 for this question the answer is that it diverges.

Step-by-step explanation:

It was on the unit test review for edge and the answer was that it diverges.

8 0

2 years ago

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Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?

VikaD [51]

This one.

The doubly-shaded area is the solution set. The dashed line is not included.

3 0

3 years ago

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You were testing orange juice recipes it’s recipe calls for orange juice concentrate and water mix one has 4 cups of concentrate

Sav [38]

Answer:

First mixed is the most orangey.

Step-by-step explanation:

First:

$Orange\ juice\ concentrate=4\ cups\\\\Water=6\ cups\\\\Tota\ content=4+6=10\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{4}{10}\times 100=40\%$

Second:

$Orange\ juice\ concentrate=1\ cups\\\\Water=3\ cups\\\\Tota\ content=1+3=4\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{1}{4}\times 100=25\%$

Third:

$Orange\ juice\ concentrate=2\ cups\\\\Water=4\ cups\\\\Tota\ content=2+4=6\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{2}{6}\times 100=33.33\%$

First mixed has highest percentage of orange juice. Hence first mixed is the most orangey.

4 0

2 years ago

WRITE AN EQUATION 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students we

Ad libitum [116K]

Answer: 54 students in each bus

Step-by-step explanation:

331 - 7 = 324

324 ÷ 6 = 54.

There were 54 students in each bus.

3 0

2 years ago

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