Question

The function f(t) = 930(0.9965) represents the change in a quantity over t hours. What does the constant 0.9965 reveal about the rate of change of the quantity?​

Answer 1

The constant 0.9965 is the rate of change per hour. Specifically, it represents the factor by which the quantity changes every hour. In this case, the factor is less than 1, indicating that the quantity is decreasing over time.

To see how this rate of change works, consider an example:

If the initial quantity is 930, after one hour the quantity will be:

f(1) = 930(0.9965) ≈ 926.20

That is, the quantity has decreased by a factor of 0.9965, or about 0.35%.

After two hours, the quantity will be:

f(2) = 930(0.9965)^2 ≈ 922.42

That is, the quantity has decreased by a factor of 0.9965 twice, or about 0.70%.

So the constant 0.9965 reveals the rate of change of the quantity, which is a decrease of about 0.35% per hour.