Question

Each day 1/2 of the money that is in bank value is removed. No money is added to the value. Which of the following represent the situation?
A. linear function with a negative rate of change
B. linear function with a positive rate of change
C. exponential decay function
D. exponential growth function

Answer 1

Answer:

Option C. exponential decay function

Step-by-step explanation:

In this problem we have a exponential function of the form

$y=a(b^x)$

where

y ---> is the money that is in the bank

x ----> number of days

a ---> is the initial value or y-intercept

b is the base of the exponential function

r ---> is the rate of change

b=(1+r)

In this problem we have that

Each day 1/2 of the money that is in bank value is removed

so

$r=-50\%=-50/100=-0.50$ ---> is negative because is a decreasing function

The value of b is equal to

$b=1-r=1-0.50=0.50$

$y=a(0.50^x)$

The value of b is less than 1

b<1

That means -----> Is a exponential  decay function