Question

on the first day of a new movie release, 783 people watched the movie at palace theaters. each day after the release, the number of people who watched the movie at palace theaters decreases by 5%. which function represents the number of people who watched the movie t days after the release? a. w(t) = 783(1.05)^t b. w(t) = 783(0.05)^t c. w(t) = (783)(0.95)t d. w(t) = 783(0.95)^t

Explanation:

Step1: Recall the exponential decay formula

The general form of an exponential decay function is \( W(t) = a(1 - r)^t \), where \( a \) is the initial amount, \( r \) is the rate of decrease (in decimal form), and \( t \) is the time.

Step2: Identify the values of \( a \) and \( r \)

Here, the initial number of people \( a = 783 \). The rate of decrease \( r = 5\% = 0.05 \). So, \( 1 - r = 1 - 0.05 = 0.95 \).

Step3: Substitute the values into the formula

Substituting \( a = 783 \) and \( 1 - r = 0.95 \) into the exponential decay formula, we get \( W(t)=783(0.95)^t \).

Answer:

D. \( W(t) = 783(0.95)^t \)