Question

1. consider the function $y = 0.54(0.3)^x$. 14a identify what type of function this is: the correct option was b exponential growth exponential decay b 5 well done! 14b what is the rate of decay? = enter your next step here

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential decay function is \( y = a(1 - r)^x \), where \( a \) is the initial amount, \( r \) is the decay rate, and \( (1 - r) \) is the decay factor. The given function is \( y = 0.54(0.3)^x \).

Step2: Compare with general form

In the given function, the base of the exponent is \( 0.3 \), which corresponds to \( (1 - r) \) in the general exponential decay formula. So we set \( 1 - r = 0.3 \).

Step3: Solve for \( r \)

To find \( r \), we rearrange the equation: \( r = 1 - 0.3 \).
Calculating this, we get \( r = 0.7 \) or \( 70\% \).

Answer:

The rate of decay is \( 0.7 \) (or \( 70\% \)).