Question

The value of a car that depreciates over time can be modeled by the function M(t)=10000(0.9)^3t+2. Write an equivalent function of the form M(t)=ab^t.

Answer 1

Answer:

  M(t) = 8100(0.729^t)

Step-by-step explanation:

You want to write M(t) = 10000(0.9)^(3t+2) in the form M(t) = ab^t.

Rules of exponents

We need to make use of a couple of rules of exponents:

  a^(bc) = (a^b)^c
  a^(b+c) = (a^b)(a^c)

Rewrite

These rules let us rewrite the equation as ...

  $M(t)=10000(0.9)^{3t+2}=10000(0.9^3)^t(0.9^2)\\\\\boxed{M(t)=8100(0.729)^t}$