Question

The value of a car that depreciates over time can be modeled by the function M(t)=18000(0.9)^{2t}.M(t)=18000(0.9) 2t . Write an equivalent function of the form M(t)=ab^t.M(t)=ab t .

Answer 1

The equivalent function in the form M(t) = ab^t for the given car depreciation function M(t) = 18000(0.9)^{2t} is M(t) = 18000(0.81)^t, achieved by squaring the base of the exponential term to fit the desired format.

Step-by-step explanation:

The question is asking to rewrite the given depreciation function M(t) = 18000(0.9)^{2t} into an equivalent function of the form M(t) = ab^t. To do this, we need to consider how exponents work with multiplication. In the original function, we have a base of 0.9 being raised to the power of 2t, which can be rewritten as (0.9^2)^t or (0.81)^t since 0.9 squared is 0.81. Thus, the equivalent function would be M(t) = 18000(0.81)^t, which fits the requested format of ab^t, where a is the initial value and b is the base of the exponential function.