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A maintenance worker in a factory notices that a water tank is leaking. She records the amount of water in the tank each day in a table

day | water (l)
———————
1 | 16,000
———————
2 | 12,000
———————
3 | 9,000
———————
4 | 6750

Write an explicit formula to represent the pattern shown in the table.

Respuesta :

The exponential function that represents this pattern is:

[tex]l = 16000(0.75)^{d-1}[/tex]

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An exponential function is represented in the following format:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change.

In this problem:

  • We consider the initial value to be 16000 in day one(not zero), thus [tex]a = 16000, x = d-1[/tex].
  • Each day, the amount is 75% of the previous day, that is, [tex]b = 0.75[/tex]

Thus, the equation is:

[tex]l = 16000(0.75)^{d-1}[/tex]

A similar problem is given at https://brainly.com/question/23416643

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