Answer:
The cost in 7 years will be of $384.69.
Step-by-step explanation:
Equation for exponential decay:
The equation for an amount after t years is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial value and r is the decay rate.
The cost of High Definition television now averages $1200, but the cost is decreasing by about 15% percent per year.
This means that [tex]A(0) = 1200, r = 0.15[/tex]. So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 1200(1-0.15)^t[/tex]
[tex]A(t) = 1200(0.85)^t[/tex]
What will the cost be in 7 years?
This is A(7).
[tex]A(t) = 1200(0.85)^t[/tex]
[tex]A(7) = 1200(0.85)^7 = 384.69[/tex]
The cost in 7 years will be of $384.69.
