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Answer :
Final answer:
The equivalent depreciation function for a car given the initial function m(t)=10000(0.9)^(3t+2) is m(t)=10000\u00b7(0.9)^3t. The correct option is b.
Explanation:
The student is asking to rewrite the depreciation function m(t) = 10000(0.9)^(3t+2) in an equivalent form without the constant added to the exponent. The value of a car that depreciates over time can be modeled using an exponential function. The goal is to express the function so that the exponent only has the variable t multiplied by a constant.
Looking at the options provided, we note that the function needs to retain the same base (0.9) and initial value (10000). To rewrite the function, we need to use the properties of exponents. We can separate the exponent 3t+2 into two parts: 3t and 2. By doing so, we can express the function in the form of m(t) = ab^t.
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