Find the exponential function f ( x ) = a^ x that passes through the point ( 2 , 1 /25 ) and has a y-intercept of 1.

Answer 1

f(x) = a^x

passes through the point (2, 1/25), meaning f(2) = 1/25

Then x=2.

f(2) = a² = 1/25

a² = (1/5)²

a = 1/5

If a is not equal to zero, it means that the y-intercept is 1 because any number(except zero) raise to zero is one.

Therefore your exponential function is:

f(x) = (1/5)^x