An exponential function of the form f(x) = ab^x passes through the points (0, 5) and (2, 5/16). What is the equation of the function?

Question

An exponential function of the form f(x) = ab^x passes through the points (0, 5) and (2, 5/16). What is the equation of the function?

Answer 1

f(x) = a(b^x)

Since f(0) = 5, a(b⁰) = 5, a = 5.

So, f(x) = 5(b^x)

Since f(2) = 5/16, 5b² = 5/16.

b² = 1/16

b = 1/4

f(x) = 5(1/4)^x