Write an exponential function in the form y = ab" that goes through points (0,7)
and (9,3584).

Step-by-step explanation:

I'm going to  assume you meant y = ab^x. If this is not correct, leave a comment.

x = 0

y = 7

7 = a * b^0

anything to the zero power is 1

y = a*b^0

y = a*1

7 = a

So far what you have is

y = 7 * b^x

Now let

x = 9

y = 3584  

3584 = 7 * b^9         Divide by 7

3584/7 = b^9

512 = b^9

If you knew how to use logs, that would be the surest way to do this question. However I'm going to make an assumption again and assume that you have not taken those yet.

So the easiest way is to find out what raised to the 9th power will equal 512

Could b = 5?

5^9 = 1 million 9 hundred thousand something. 5 is far too big. Make sure you understand why. 1 million is far greater than 512

So let's try b = 3

3^9 = 19 thousand which is still far too big. 19 thousand something is far larger than 512.

We have just one more number that we can try.

2^9 = 512 and we have it

Answer y = 7*2^x

answer: 7270

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕