Question

A quantity decays at a weekly continuous rate of 12.7%. What is this quantity's weekly decay rate?

Answer 1

The weekly decay rate of the quantity is approximately 0.1206 or 12.06%.

Step-by-step explanation:

The continuous decay of a quantity can be modeled using the exponential decay formula:
`\(N(t) = N_0 \cdot e^(-rt)\)`, where N(t) is the quantity at time t, N_0is the initial quantity, r is the decay rate, and e is the base of the natural logarithm.

In this case, we are given that the quantity decays at a weekly continuous rate of 12.7\%. To find the 100, and since it's a decay, the rate is negative. Therefore, r = -0.127.

Now, we have the exponential decay formula as
`\(N(t) = N_0 \cdot e^(-0.127t)\).` The decay rate is the coefficient of t in the exponent, which is -0.127.

The percentage form of the decay rate is found by multiplying the coefficient by 100, giving-12.7\%. So, the weekly decay rate is 12.7% or, in decimal form, approximately 0.1206 or 12.06%.