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Tpy6a [65]
3 years ago
5

Oxford currently generates 45,000 tons of garbage per year. but the city is launching some recycling initiatives to bring that n

umber 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)
Mathematics
1 answer:
barxatty [35]3 years ago
8 0

Answer:

-Exponential Decay

-Decay factor is (1-0.05)

Step-by-step 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)

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