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RoseWind [281]
3 years ago
14

Which of the following exponential functions goes thru points (1,6) and (2,12)

Mathematics
1 answer:
Alexandra [31]3 years ago
7 0

Answer:

Noting that e^b = 6/a

Step-by-step explanation:

Use the general expo function y = ae^(bx).

Subbing 6 for y and 1 for x, we get  6 = ae^(b), or   e^b = 6/a.

Subbing 12 for y and 2 for x, we get   12 = ae^(2b), or 12/a = (e^b)²

Now let's find the value of the coefficient a.  Noting that e^b = 6/a, rewrite

12/a = (e^b)² as 12/a = (6/a)².

Dividing both sides by 6/a, we get 2 = 6/a, or a = 3.

Again Noting that e^b = 6/a, e^b = 6/3, or e^b = 2.

Taking the natural log of both sides, we get b = ln 2.

Then our y = ae^(bx) becomes:

                y = 3e^(ln 2·x), or   y = 3·2^x

Note:  next time, please share the answer choices.  Thank you.

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Answer:

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Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
aev [14]

Answer:

y=4sin(\frac{\pi}{2} x+\pi)-2

Step-by-step explanation:

The equation of a periodic  function is in the form:

y = Asin(Bx + C) + D

Where A = amplitude, B = 2π / period, D = vertical shift, phase shift = -C / B.

Given that:

amplitude: 4, period 4 phase shift = vertical shift = -2

Hence:

A = amplitude = 4, B = 2π / period = 2π / 4 = π / 2, D = vertical shift = -2.

Phase shift = -C / B

C = -phase shift * B = - * -2 * π / 2 = π.

Therefore substituting gives:

y=4sin(\frac{\pi}{2} x+\pi)-2

8 0
3 years ago
Can someone fr help me with this like right now i’ll appreciate it sm
rjkz [21]

Step-by-step explanation:

Since

\frac{108}{72}  =  \frac{3}{2}

\frac{72}{48}  =  \frac{3}{2}

\frac{48}{32}  =  \frac{3}{2}

The function has a constant factor so we have a exponential function.

The equation of a exponential function is

y = a(b) {}^{x}

Where a is the initial value and b is the growth factor

The growth factor is 3/2,

The initial value in 32

y =  32 ( \frac{3}{2} ) {}^{x}

Plug in 4 for x.

You will get 162

Plug in 5 for x you will get

243.

2013- 162

2014- 243

8 0
1 year ago
Using the answers from z^4=16 determine the solutions of the equation (x+1)^4=16(x-1)^4​
Artemon [7]

i hope i have been useful buddy.

good luck ♥️♥️♥️♥️♥️.

4 0
3 years ago
CAN SOMEONE PLEASE HELP ME???
Varvara68 [4.7K]

Answer:

m=2

Step-by-step explanation:

slope is the average rate of change in a specific interval

we can calculate slope in this case with Δy/Δx or (y2-y1)/(x2-x1)

m=(y2-y1)/(x2-x1)

=(-1-7)/(-3-1)

=-8/-4

=2

5 0
2 years ago
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