Question

1. in the function $g(x) = 2 \cdot (1.5)^x$, what is the initial value?

a. 2
b. $x$
c. 1.5
d. 3

Explanation:

Step1: Recall the form of an exponential function

The general form of an exponential function is \( g(x) = a \cdot b^x \), where \( a \) is the initial value (the value of the function when \( x = 0 \)) and \( b \) is the base (the growth or decay factor).

Step2: Identify the initial value in the given function

In the function \( g(x)=2\cdot(1.5)^x \), we compare it to the general form \( g(x) = a \cdot b^x \). Here, \( a = 2 \) and \( b = 1.5 \). So the initial value (the value of \( a \)) is 2.

Answer:

a. 2