Question

strontium - 90 is a radioactive material that decays according to the function ( a(t)=a_{0}e^{-0.0244t} ), wh
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 ( -2.44% ).
(type an integer or a decimal. include the negative sign for the decay rate.)
(b) approximately 302 grams of strontium - 90 is left after 40 years.
(do not round until the final answer. then round to the nearest whole number as needed.)

Explanation:

Step1: Substitute values into formula

Given \(A(t)=A_{0}e^{-0.0244t}\), \(A_{0} = 800\), \(t = 40\).
\(A(40)=800e^{-0.0244\times40}\)

Step2: Calculate exponent

\(-0.0244\times40=-0.976\)
\(A(40)=800e^{- 0.976}\)

Step3: Calculate exponential value

Using \(e^{-0.976}\approx0.3775\)
\(A(40)=800\times0.3775\)

Step4: Calculate final result

\(800\times0.3775 = 302\)

Answer:

\(302\)