I need help solving this math problem.

Use the equation of the exponential function whose graph passes through the points (0,-2) and (2,-50) to find the value of y when x=-2

A. -1/100. B. 50
C. -2/25. D. -1/50

I keep getting an answer that's not even one of my choices. Please help and explain how you got your answer because I'm trying to study for my exam and this is one of the types of questions we are recommended to understand.

An exponential function is in the form y = a * b^x, where a and b are positive numbers. Since we have two points (x,y), we can solve for a and b:

(0, 2) means that x = 0, y = -2:
y = a * b^x
-2 = a * b^0
-2 = a (because b^0 = 1)

(2, -50) means that x = 2, y = -50, AND we now know that a = -2, so we can plug in all of those values:
y = a * b^x
-50 = -2 * b^2
25 = b^2
b = 5 (NOT -5 because b is always a positive number).

Therefore, the entire exponential function is: y = -2 * 5^x

When x = -2, y = -2 * 5^(-2) = -2 * (1/25) = -2/25. The answer is C.

a general form of an exponential function is y=Ae^(kx)
using 1st point (0,-2) gives -2 =A e^0=A so y=-2e^(kx)
using 2nd point (2,-50) gives -50=-2e^2k ie 25 =e^2k
when x=-2 y=-2e^-2k = -2/e^2k=-2/25 so y=-2/25

you want f(0)=-2 and f(2)=-50
since its exponential you are going to use the form a^x
-a^0 + c = -2
-1 + c = -2
c = -1
-a^2 -1 = -50
-a^2 = -49
a^2 = 49
a = 7
f(x)= -7^x -1
f(-2)=-7^-2 - 1= -1/50

i would pick B because it is the only one that isnt a point