Question

strontium - 90 is a radioactive material that decays according to the function ( a(t)=a_{0}e^{-0.0244t} ), where ( a_{0} ) is the initial
assume that a scientist has a sample of 800 grams of strontium - 90.
(a) what is the decay rate of strontium - 90?
(b) how much strontium - 90 is left after 40 years?
(c) when will only 600 grams of strontium - 90 be left?
(d) what is the half - life of strontium - 90?
(a) the decay rate of strontium - 90 is (square%).
(type an integer or a decimal. include the negative sign for the decay rate.)

Explanation:

Step1: Recall the exponential decay formula

The general form of exponential decay is \(A(t)=A_0e^{rt}\), where \(r\) is the decay rate. In the given function \(A(t) = A_0e^{- 0.0244t}\), comparing with the general form, we can identify the value of \(r\).

Step2: Convert the decay rate to a percentage

To convert the decimal value of \(r\) to a percentage, we use the formula \(r(\text{percentage})=r\times100\).

Answer:

The decay rate of strontium - 90 is \(-2.44\%\)