Question

Oxford currently generates 45,000 tons of garbage per year. but the city is launching some recycling initiatives to bring that number down. If as a result, the amount of garbage decreases by 5% each year. Is this problem exponential growth or decay? Identify the growth or decay factor.

growth, (1 + .05)
growth, (1-.05)
decay,(1+.05)
decay,(1-.05)

Answer 1

-Exponential Decay

-Decay factor is (1-0.05)

Explanation:

-Given that the number decreases by a defined rate each year from the initial size by 5%,

-This is an exponential decay function of the form:

`y=Ae^(-rt)`

Where:

`y` is the quantity/size after time t

`A` is the initial size

`r` is the rate of decay

-Our function can the be written as

`y=45000e^(-0.05t)`

Hence, the decay rate/factor is 0.05

#Alternatively

The exponential decay can be of the form:

`y=ab^x`

Where:

y is the size at time x, a is the initial size, x is time and b is the decay factor.

b is of the form
`b=(1-r),\ \ r=decay\ rate`

`y=ab^x\\\\y=45000(1-0.05)^x`

Hence, the decay factor is (1-0.05)