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The function [tex]f(t) = 360(0.9935)^{t}[/tex] represents the change in a quantity over [tex]t[/tex] months. What does the constant 0.9935 reveal about the rate of change of the quantity?

Answer :

Final answer:

The constant 0.9935 in the function indicates that the quantity is decreasing by 0.65% each month. This is the rate of change.

Explanation:

In the function f(t)=360(0.9935)^(t), the constant 0.9935 is the base of the exponential expression. This constant indicates the rate of change of the quantity over time. Specifically, it tells us that the quantity is decreasing by about 0.65% each month because 1 - 0.9935 equals 0.0065 or 0.65% when expressed as a percentage. Therefore, every month, the quantity gets smaller because it's multiplied by 0.9935, a value less than 1.

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