Questions: Does the function f(x)=0.2(1.21)^x represent exponential growth decay, or neither? The function represents exponential growth because b>1. The function represents exponential growth because 0<b<1. The function represents exponential decay because b>1. The function represents exponential decay because 0<b<1. The function represents neither because a<1. The function represents neither because it is not exponential.

Solution Steps

To determine whether the function \( f(x) = 0.2(1.21)^x \) represents exponential growth or decay, we need to examine the base of the exponential term, which is 1.21. If the base \( b \) is greater than 1, the function represents exponential growth. If \( 0 < b < 1 \), it represents exponential decay. In this case, since 1.21 is greater than 1, the function represents exponential growth.

The given function is \( f(x) = 0.2(1.21)^x \). This is an exponential function where the base is \( b = 1.21 \).

To determine whether the function represents exponential growth or decay, we analyze the base \( b \):

• If \( b > 1 \), the function represents exponential growth.
• If \( 0 < b < 1 \), the function represents exponential decay.

In this case, since \( b = 1.21 \) and \( 1.21 > 1 \), we conclude that the function represents exponential growth.

Final Answer