Question

Decide if the function y = (1/16)(-x^2) is an exponential growth function or an exponential decay function. Describe its end behavior using limits.

Answer 1

The function y = (1/16)(-x^2) is an exponential decay function. Its end behavior is that it approaches positive infinity as x approaches negative infinity, and it approaches 0 as x approaches positive infinity.

Step-by-step explanation:

The function y = (1/16)(-x^2) is an exponential decay function. In an exponential decay function, the base of the exponential term is between 0 and 1. In this case, the base is (1/16), which is less than 1, indicating decay.

To describe its end behavior using limits, we take the limit as x approaches positive infinity and as x approaches negative infinity:

lim(x->-∞) [(1/16)(-x^2)] = ∞

lim(x->∞) [(1/16)(-x^2)] = 0

As x approaches negative infinity, the function approaches positive infinity (increases without bound), while as x approaches positive infinity, the function approaches 0.