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Express the value of Plane Y as an exponential function similar to the one given for the value of Plane X
above, except the time will be m months after purchase. (Use b(m) for the value of Plane Y in thousands
of dollars). Provide evidence to support your answer.

Express The Value Of Plane Y As An Exponential Function Similar To The One Given For The Value Of Plane X Above Except The Time Will Be M Months After Purchase class=

Sagot :

The exponential function for plane Y is given by:

[tex]A(t) = 181581(0.976)^t[/tex]

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, the monthly depreciation rate is of 2.4%, hence r = 0.024 and:

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

[tex]A(t) = A(0)(1 - 0.024)^t[/tex]

[tex]A(t) = A(0)(0.976)^t[/tex]

One month after, we have that A(1) = 177223, hence:

[tex]A(t) = A(0)(0.976)^t[/tex]

[tex]177223 = 0.976A(0)[/tex]

[tex]A(0) = \frac{177223}{0.976}[/tex]

[tex]A(0) = 181581[/tex]

Hence, the equation is:

[tex]A(t) = 181581(0.976)^t[/tex]

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

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