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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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Find parametric equations which describe each curve. No particular orientation is required.
MA_775_DIABLO [31]

Answer:

The equation of the line is (x(t),y(t))=(1-4t,2+6t) and the equation of the circle is F(t)= (3cos(t)+4,3sin(t)+1).

Step-by-step explanation:

(a) Given: The given points are (1,2) and (-3,8).

To find: The parametric equation of line containing points (1,2) and (-3,8).

We know that the parametric equation of line containing (x_{1} ,y_{1} ) and (x_{2} ,y_{2} ) is given by (x(t),y(t))=(x_{1}+(x_{2}-x_{1})t,y_{1}+(y_{2}-y_{1})t) where t∈[0,1].

Now, x(t)=1+(-3-1)t

i.e, x(t)=1-4t

And, y(t)=2+(8-2)t

i.e, y(t)=2+6t

Hence, the required parametric equation of the line is (x(t),y(t))=(1-4t,2+6t).

(b) Given: The radius of circle is 3 and centre is (4,1).

To find: The parametric equation of circle with radius 3 and centre (4,1).

We know that parametric equation of circle with radius r and centre (h,k) is given by F(t)= (x(t),y(t)) where x(t)=rcos(t)+h and y(t)=rsin(t)+k.

Now, x(t)=3cos(t)+4

y(t)=3sin(t)+1

So, the parametric equation of circle having radius 3 and centre (h,k) is F(t)= (3cos(t)+4,3sin(t)+1).

Hence, the required equation of the circle is F(t)= (3cos(t)+4,3sin(t)+1).

7 0
2 years ago
An airplane has flown 260 miles out of a total trip of 500 miles.what fraction in simplest form of the trip has been completed?
lakkis [162]

i believe that the answer is 13/25

3 0
3 years ago
I think the answer is 6 but can someone check if im correct
OleMash [197]

Answer:

5

Step-by-step explanation:

i dont see how you get 6 but it's 5

8 0
2 years ago
100e^0.125t=200<br><br>A. t= ln(16)<br>B. t= ln(256)<br>C. t= 8ln(100)<br>D. t= 0.08ln(200)
Drupady [299]

The correct answer is C. t= 8ln(100)

Hope this helped! :)



^-^

5 0
3 years ago
There were 8 finalists in the Atlantic County spelling bee and 12 finalists in the Ocean County spelling bee. If one finalist fr
wolverine [178]
I think it is A
Hope this help you
4 0
2 years ago
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