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Miranda deposits $100 into a savings account. she decides that she will make one deposit at the end of each month and that she will increase the amount that she deposits by 10% each month.


a. complete the table to show the amount of money miranda deposits at the end of each month for the first 4 months

Respuesta :

Using an exponential function, it is found that the amounts deposited at the end of each month are given by:

  • At the end of the first month, she deposits $110.
  • At the end of the second month, she deposits $121.
  • At the end of the third month, she deposits $133.1.
  • At the end of the fourth month, she deposits $146.41.

What is an exponential function?

An increasing 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 growth rate, as a decimal.

In this problem, we have that A(0) = 100, r = 0.1, hence the equation for the amount deposited after t months is:

[tex]A(t) = 100(1.1)^t[/tex]

Then, for each of the first four months:

  • [tex]A(1) = 100(1.1)^1 = 110[/tex]
  • [tex]A(2) = 100(1.1)^2 = 121[/tex]
  • [tex]A(3) = 100(1.1)^3 = 133.1[/tex]
  • [tex]A(4) = 100(1.1)^4 = 146.41[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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