Question

for the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. if q(0) = 14, which equation defines q? a q(x)=0.55(14)^x b q(x)=1.45(14)^x c q(x)=14(0.55)^x d q(x)=14(1.45)^x

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential decay function is \( q(x) = a(1 - r)^x \), where \( a \) is the initial value, \( r \) is the rate of decrease (as a decimal), and \( x \) is the independent variable.

Step2: Identify initial value and decay rate

Given \( q(0) = 14 \), so the initial value \( a = 14 \). The value decreases by 45%, so the remaining percentage is \( 1 - 0.45 = 0.55 \).

Step3: Substitute into the formula

Substituting \( a = 14 \) and \( 1 - r = 0.55 \) into the exponential decay formula, we get \( q(x) = 14(0.55)^x \).

Answer:

C. \( q(x) = 14(0.55)^x \)