Answer:
b) f(x)=200-100x^2
Explanation:
I answered section b, because if you know the equation, you can find the other values by plugging x into the equation.
We know that this function is exponential, that means that somewhere in the function there will be a "x^2" [f(x)=x^2]
if f(0)=200, then the constant in the equation is 200. [f(x)=200+x^2]
Since the value of f(1)=100, that means that the the the parabola faces downwards, which means the value attached to the x value will be negative. [f(x)=200-x^2]
If you just use this equation, the values will never add up, so there's still something missing. In this case, the scale of the x value is off, so there needs to be a number x^2 is multiplied by. if we rewrite the function as f(x)=200-b*x^2 and plug in the values (1,100):
100=200-b*1^2
and solve for b, we will see that b=100.
So the function is f(x)=200-100x^2