Algebra-1

The function f(x) = a · b^x represents exponential growth if b > 1. The parameter 'a' is a constant that affects the vertical stretch or shift of the graph, but it does not impact the growth rate determined by 'b'.

When b = 2, the function can be represented as f(x) = a ⋅ 2^x . As x increases, f(x) increases at a certain rate.

When b = 3, the function becomes f(x) = a ⋅ 3^x . The increase in base leads to a faster rate of growth.

Comparing Growth Rates:

At x = 1:
f(1) = a ⋅ 2¹ = 2a
f(1) = a ⋅ 3¹ = 3a

At&nb...