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Households in a city produced a total of 125 000 tonnes of waste in 2017. The total amount of waste is expected to fall by 2% each year.


Calculate the total amount of waste these households are expected to produce in 2020.


(3 marks)

Sagot :

Using an exponential function, it is found that the total amount of waste these households are expected to produce in 2020 is of 117,649 tones.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem, we have that:

  • The households produced a total of 125 000 tonnes of waste in 2017, hence A(0) = 125000.
  • The total amount of waste is expected to fall by 2% each year, hence r = 0.02.

Thus, the equation is:

[tex]A(t) = 125000(1 - 0.02)^t[/tex]

[tex]A(t) = 125000(0.98)^t[/tex]

2020 is 3 years after 2017, hence the amount is:

[tex]A(3) = 125000(0.98)^3 = 117649[/tex]

The total amount of waste these households are expected to produce in 2020 is of 117,649 tones.

You can learn more about exponential functions at https://brainly.com/question/25537936

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