Question

Which of the following functions represents exponential growth?

y = 1/2 (3)^x
y = 1/2 x^2
y = 2(1/3)^x
y = 2x^1/2

Answer 1

Exponential growth occurs for functions of the form y = a·b^x with base b > 1.

Only y = (1/2)·3^x is exponential growth (base 3 > 1).

- y = (1/2)x^2 is a polynomial (quadratic), not exponential.
- y = 2(1/3)^x is exponential but with base 1/3 < 1, so it is exponential decay.
- y = 2x^(1/2) = 2√x is a power function, not exponential.