+318 Write an equation of the form a^x+b.... Then compute f(2)
It gives the two points in the graph =(-2,21) and (-1,1)
f(x)=_______________
f(2)=
+23252 If the equation is of the form: y = ax + b
(-2, 21) ---> 21 = a-2 + b ---> solving for a: a-2 = 21 - b
(-1, 1) ---> 1 = a-1 + b ---> solving for a: a-1 = 1 - b ---> (a-1)2 = (1 - b)2 ---> a-2 = 1 - 2b + b2
Setting these two equal to each ohter: 1 - 2b + b2 = 21 - b
b2 - b - 20 = 0
(b - 5)(b + 4) = 0 ---> b = 5 or b = -4
Since a-1 = 1 - b ---> 1/a = 1 - b ---> a = 1/(1 - b)
If b = 5, then a = 1/(1 - 5) = 1/-4 = -0.25 [But, if you have a negative base, you won't have a continuous function.]
If b = -4, then a = 1/(1 - -4) = 1/5 = 0.20
y = (0.20)x - 4
