An exponential function f(x) = ab" passes through the points (0, 12000) and (2, 3000). What are the values of a and b ?

Given:

An exponential function passes through the points (0, 12000) and (2, 3000).

To find:

The values of a and b.

Solution:

We have,

     ...(i)

It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get

Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get

Taking square root on both sides.

For an exponential function b cannot be negative. So, .

Therefore, the value of a is 12000 and the value of b is .

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3