Question

24
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)(0.95)t )
b. ( w(t) = 783(0.95)^t )
c. ( w(t) = 783(1.05)^t )
d. ( w(t) = 783(0.05)^t )

Explanation:

Step1: Identify decay model type

This is exponential decay, formula: $W(t) = W_0(1-r)^t$, where $W_0$ = initial amount, $r$ = decay rate.

Step2: Define given values

$W_0 = 783$, $r = 0.05$, so $1-r = 0.95$.

Step3: Substitute into formula

$W(t) = 783(0.95)^t$

Step4: Match to options

This matches option B.

Answer:

B. $W(t) = 783(0.95)^t$