+318 Write an equation of the form f(x)=a^x+b
with these two points: (-2,-2) and (-1,-4) PLEASE HELP
then compute f(2)
appreciate sending me links but ive tried this problem so many times and an answer is what im looking for... thanks
+129852 We have these two equations
a^(-2) + b = -2
a^(-1) + b = -4 subtract the second equation from the first
a^(-2) - a^(-1) = 2 and we can write
1/a^2 - 1/a = 2 rearrange as
1/a^2 - 1/a - 2 = 0 factor as
(1/a + 1) ( 1/a - 2) = 0
Set each factor to 0 and solve for a
1/a + 1 = 0 1/a - 2 = 0
a = - 1 1/a = 2
a = 1/2
This is an exponential function, so a must be positive
So we have that
a^(-2) + b = -2
(1/2)^(-2) + b = -2
4 + b = -2
b = -6
So
f(2) = (1/2)^2 - 6 = 1/4 - 6 = -23/4
