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 an 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 ( square ) 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 the formula

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

Step2: Calculate the exponent

First, calculate \(-0.0244\times40=-0.976\)
Then \(A(40)=800e^{- 0.976}\)

Step3: Calculate the value of \(e^{-0.976}\)

We know that \(e^{-x}=\frac{1}{e^{x}}\), so \(e^{-0.976}\approx0.3769\)

Step4: Calculate \(A(40)\)

\(A(40)=800\times0.3769 = 301.52\)

Answer:

\(302\) grams