find the exponential model y= ae^bx that fits the two points.?

Question

the points are (0,4) and (5, 1/2)
need to know how to do it. plz explain.

Answer 1

When x = 0, then e^bx must be one because b*x = 0, and e^0 = 1. So, a must be equal to whatever y there is for that x. In this case, a=4.

Then, by substituting in the other numbers, the equation can be solved: y = 1/2 = 4*e^(b*5)
ln(1/8) = b*5
b = ln(1/8) / 5

So, your final model is y = 4*e^(x*ln(1/8)/5)

Answer 2

4 = a*e^0 =a .So a=4

1/2 = 4 *e^5b => e^5b=1/8 ===> 5b =-Ln8 So b=-(Ln 8)/5