write an exponential function whose graph passes throught the given points... (0,3)and (1,15)...(0,-5)and(-3,-135)...(0,-0.3)and(5,-9.6)

Why did you list them as three pairs of two ponts? What do you mean by an exponential equation? A polynomial? Does it have to pass through all six points?

To write an exponential function that passes through two points, we can use the general form of an exponential function:

f(x) = a * b^x

Using the given points, we can substitute the x and y values into the equation to create a system of equations:

(1) 3 = a * b^0
(2) 15 = a * b^1

Simplifying equation (1) gives us a = 3, so we can substitute this value into equation (2):

15 = 3 * b^1
5 = b

Therefore, the exponential function that passes through the points (0,3) and (1,15) is:

f(x) = 3 * 5^x

Similarly, we can apply the same process to find the exponential functions for the other given points:

For (0,-5) and (-3,-135):

(3) -5 = a * b^0
(4) -135 = a * b^(-3)

By simplifying equation (3), we find a = -5, which we can substitute into equation (4):

-135 = -5 * b^(-3)
27 = b^(-3)
b = 1/3

Therefore, the exponential function that passes through the points (0,-5) and (-3,-135) is:

f(x) = -5 * (1/3)^x

Finally, for (0,-0.3) and (5,-9.6):

(5) -0.3 = a * b^0
(6) -9.6 = a * b^5

By simplifying equation (5), we find a = -0.3, which we can substitute into equation (6):

-9.6 = -0.3 * b^5
32 = b^5
b = 2

Therefore, the exponential function that passes through the points (0,-0.3) and (5,-9.6) is:

f(x) = -0.3 * 2^x