Answer :
Final answer:
The given function y=3700(0.97)^x is a typical form of the exponential decay function and it implies a 3% decrease in the value of y for each unit increase of x. This function can model various situations in which values decrease over time, like a car's depreciation or radioactive decay.
Explanation:
The student's question pertains to the properties of the exponential function y=3700(0.97)^(x). This is a typical form of the exponential decay function, where 3700 is the initial value (the value of 'y' when 'x' equals zero), 0.97 is the base, which represents a 3% decay rate (100% - 97%), and 'x' is the exponent, usually representing time.
The function indicates that the value of y decreases or decays over time at a rate of 3% per unit of x. This could be applied in various scenarios, such as the depreciation of a car's value over time, or the decay of a radioactive substance.
To find the percentage rate of change, you need to subtract 1 from the base value and then multiply the result by 100. So, for this function, the percentage rate of change is (0.97 - 1) * 100 = -3%. This means that the value of 'y' decreases by 3% for each increase in 'x'.
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