Question

What is the rate of decay for the function f(x) =2(0.95)^x ( x is on top of the parentheses)

Answer 1

The decay rate is 5%.

Explanation:

Let a substance is decaying at the rate of r% per hour from the initial value of P for t hours, then the final value of the substance is given by the function

`f(t) = P(1 - (r)/(100))^(t)` ........... (1)

Comparing this equation with the original equation given as

`f(x) = 2(0.95)^(x)` ............ (2) we get,

`(1 - (r)/(100)) = 0.95`

⇒
`(r)/(100) = 0.05`

⇒ r = 5%.

Therefore, the decay rate is 5%. (Answer)