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ale4655 [162]
3 years ago
15

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

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
6 0

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}.

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lutik1710 [3]

Answer:

$7.50

Step-by-step explanation:

<u>If she is not a member:</u>

to print 350 pictures, she will pay 0.2 * 350 = $70

<u>If she IS a member:</u>

to print 350 pictures, she will pay 0.15(350) + 10 = $62.5

THus, the amount she saves is 70 - 62.5 = $7.50

4 0
3 years ago
Read 2 more answers
F:[1/2,infinity)—&gt;[3/4,infinity) <br> f(x)=x^2-x+1 <br> find the inverse of f(x);please explain
dexar [7]

Answer:

f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

\pm \sqrt{y-3/4}=x-1/2

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

\sqrt{y-3/4}=x-1/2

Add 1/2 on both sides:

1/2+\sqrt{y-3/4}=x

The last step is to switch x and y:

1/2+\sqrt{x-3/4}=y

y=1/2+\sqrt{x-3/4}

f^{-1}(x)=1/2+\sqrt{x-3/4}

8 0
3 years ago
The measure of an angle is 5 times as great as the measure of it's complement. Find the measure of the angle
horrorfan [7]
15 is the mesure of the angle
4 0
3 years ago
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What is the approximate surface area of the sphere if circumference is 37.68?
damaskus [11]

The surface area of a sphere is  A = 4 π R² .

Sadly, the question doesn't give you 'R', so you have to
back it out of the circumference.

                           Circumference = π (diameter)

Divide each side by π :  Diameter = circumference / π

Radius = 1/2 diameter:  Radius = circumference / (2 π)

                                       Area = 4 π R²  =

                                                 4 π (circumference/2π)² =

                                                 4 π (circumference)² / 4 π²

Divide top and bottom by  4π :  Area = (Circumference)² / π

         Circumference = 37.68 units

         Area =  (37.68)² square units /π =
    
                       <em>451.93 square units</em>


8 0
2 years ago
How to solve 64mi/h=____ft/s
MakcuM [25]
To convert miles to feet you multiply by 5280
To convert hours to seconds you divide by 3600

so you multiply 64  by 5280/3600   which comes to  93.87 ft/s Answer


7 0
3 years ago
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