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Answer :
Final answer:
The equation y = a(1.37)^x represents exponential growth with a growth factor of 1.37, where 'a' is the initial quantity and 'x' is time in years.So, the correct answer is option A.
Explanation:
The equation in question is y = a(1.37)^x, where a represents the initial value and x represents time in years. Because the base of the exponent, 1.37, is greater than 1, this equation is indicative of exponential growth. When the exponent x increases, the value of y grows exponentially, making the growth factor 1.37. This growth factor is a multiplier that shows how much a quantity increases over a set period of time, in this case, per year.
Let's break down the equation. For a being the initial amount, we can think of it as the starting point of our measurement, meaning when x = 0, y will equal a. As time passes (as x increases), the value of (1.37)^x becomes larger, multiplying the initial value a by a greater number, representing an exponential increase in y over time.
In comparison to linear growth, which has a constant rate of increase and can be described by the equation y = mx + b, exponential growth's rate of increase becomes faster as time goes on. This is directly contrasted with linear growth or decay, which has a fixed amount of change per time interval. Exponential equations demonstrate how quantities can grow very quickly, which is characteristic of phenomena such as population growth, inflation, or compound interest in finance where the concept of time value is crucial.To summarize, the correct answer is:A) It represents exponential growth with a growth factor of 1.37.
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