Question

identify the type of function represented by $f(x) = \frac{3}{8}(4)^x$. a. exponential decay b. linear c. exponential growth d. quadratic

Explanation:

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial value and \( b \) is the base. If \( b>1 \), the function represents exponential growth; if \( 0 < b < 1 \), it represents exponential decay. For the function \( f(x)=\frac{3}{8}(4)^x \), the base \( b = 4 \), which is greater than 1. So it is an exponential growth function. Linear functions have the form \( y = mx + c \) (no exponent on the variable), and quadratic functions have the form \( y=ax^{2}+bx + c \) (variable with exponent 2), so this function is not linear or quadratic. Also, since the base is greater than 1, it is not exponential decay.

Answer:

C. Exponential growth