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In 2020 Ashmija invested $10,000 into an account which is growing at 4.5% annually.

Write an equation to model the amount of money in her account D(t), with respect to time, t. Explain what the values represent. [4 Marks]

Use your equation to find how much she will make in 2050 assuming she hasn't made any withdrawals or extra deposits. [3 marks]

Respuesta :

The exponential function that models this situation is:

[tex]D(t) = 10000(1.045)^t[/tex]

Using the function, in 2050, she will have $37,453.

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.

For this problem, the parameters are:

A(0) = 10000, r = 0.045.

Hence the equation is:

[tex]D(t) = 10000(1.045)^t[/tex]

2050 is 30 years after 2020, hence the amount is:

[tex]D(30) = 10000(1.045)^{30} = 37453[/tex]

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

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