Question

A quantity with an initial value of 390 decays continuously at a rate of 5% per decade. What is the value of the quantity after 51 years, to the nearest hundredth?

Answer 1

The value of the quantity after 51 years is approximately 246.68.

Step-by-step explanation:

To find the value of the quantity after 51 years,

we can use the formula A = P(1 - r)^t, where A is the final value,

P is the initial value, r is the rate of decay, and t is the time in decades.

In this case, P = 390, r = 0.05, and t = 5.1 (since there are 10 decades in a century and 51 years is 5.1 decades).

Plugging in these values, we get A = 390(1 - 0.05)^(5.1) = 390(0.95)^(5.1) ≈ 246.68.