Suppose that the graph of f(x) = Ca^x passes through the points (2, 0.25) and (4, 0.015625).?

Substitute in the given values to get two simultaneous equations in C and a

0.25 = Ca²

0.015625 = Ca^4

Divide the second equation by the first to get (0.015625/0.25) = Ca^4/Ca² = a²

So a² = 0.0625 so that a = 0.25 = ¼

Now substitute this back into the first equation to get 0.25 = C (0.25)²

Therefore C = 0.25/(0.25)² = 4

so your formula is f(x) = 4(¼)˟ = 4¹ˉ˟