1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
e-lub [12.9K]
3 years ago
7

Find the equation of the exponential function represented by the table below:

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0

Given:

The table of values.

To find:

The equation of the exponential function represented by the table.

Solution:

The general form of an exponential function is

y=ab^x          ...(i)

where, a is initial value and b is growth factor.

From the given table it is clear that the function passes through (0,3) and (1,1.5). So, the must be satisfy by these points.

Putting x=0 and y=3 in (i), we get

3=ab^0

3=a(1)

3=a

Putting a=3, x=1 and y=1.5 in (i), we get

1.5=3b^1

\dfrac{1.5}{3}=b

\dfrac{1}{2}=b

Putting a=3 and b=\dfrac{1}{2} in (i), we get

y=3\left(\dfrac{1}{2}\right)^x

Therefore, the required equation for exponential function is y=3\left(\dfrac{1}{2}\right)^x.

You might be interested in
At the carnival, Alana gave away 26 ride tickets to her friends. She now has 57 tickets left. Let x be the number of tickets tha
umka2103 [35]
THE EQUATION IS 26 + 57 = X BECAUSE YOU ADD THE 2 NUMBERS TO GET THE VALUE WHICH IS X.
7 0
3 years ago
Ace Landscape buys 100 shovels for $15 each. Ace sells all 100 shovels at $29.99. What is his profit?
Yanka [14]
$29.99=$30
$30-$15=$15 
Ace's profit is $15
7 0
3 years ago
Please help STRUGGLING with math few math questions! Ty
-BARSIC- [3]

Question 1:


F(x) and g(x) are like variables, just plug into the equation.


f(x) + g(x) = (x + 6) + (12x - 7)


x+6+12x-7 = 13x-1


Question 2: f(3) + g(-1)


You plug in the x-values into the equation, and then take the answer and add them together.


f(3) = 3+4

g(-1) = 12(-1)-6


f(3) = 7

g(-1) = -18


7 + (-18) = -11


Question 3:


This is similar to question 1, plug in the variables and simplify.


9x - (7x+3)


Remember to distribute the "-"


9x - 7x - 3

2x - 3

6 0
3 years ago
Read 2 more answers
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S

Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by

\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k

with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is

d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}

The surface element reduces to

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv

so that it points toward the origin at any point on <em>S</em>.

Then the integral with respect to <em>u</em> and <em>v</em> is

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS

=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS

=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}

4 0
3 years ago
-12&lt;-6x please help
pishuonlain [190]
-12 < -6x

-12/-6 > x    divide both sides by -6

12/6 > x      two negatives makes a positive

2 > x            simplify

x < 2           
switch sides

hope this helps, God bless! 
6 0
3 years ago
Other questions:
  • Which table reprents a linear function
    14·1 answer
  • Help me with everything plz
    6·1 answer
  • Write an equation in point-slope form.
    8·1 answer
  • You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage. You are standing on a platfo
    5·1 answer
  • Point (2, 4) is reflected across the x-axis. What are <br> the coordinates of its image?
    11·1 answer
  • If 7x + 11 = 39, then 7x = 28.<br> Name property
    11·1 answer
  • Please help me on this i will give you brainliest
    14·2 answers
  • What is a constant?!
    12·2 answers
  • There were 27 bales of hay in the barn. Grant stacked some more bales in the barn.Now there are 76 bales. Let b be the number of
    14·1 answer
  • She is fine simple future​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!