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
