Answer:
The exponential equation is y = -2×(1/2)^x
Step-by-step explanation:
Ok we have a couple things to note here:
1) The horizontal asymptote of the function is the x axis (always nice)
2) At x=0, y=-2 (i.e, this function will be multiplied by -2 bc the exponent part will transform into one at x=0)
3) Then we need to ascertain the base of the exponential. Based on the facts that at x=1, y=-1 and the "a-value" is -2, we can set up an equation to find b:
y=a×b^x----> -1 = (-2)(b) ------> b=1/2
Therefore, the exponential equation is y = -2×(1/2)^x
Test:
At x = 0, y= -2
At x = -1, y = (-2)*(1/2)^-1 = (-2)*2 = -4
At x=2, y = (-2)*(1/2)^2= (-2)*(1/4) = -1/2
Thus we can be quite certain that this is correct
