Exponential Functions
1. 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 amount present and \(A\) is the amount present at
time \(t\) (in years). Assume that a scientist has a sample of 500 grams
of Strontium-90.
(a) What is the decay rate of Strontium-90? Explain the decay rate in context of the problem. Write a complete sentence.
(b) How much strontium-90 is left after 10 years?
(c) When will 400 grams of strontium-90 be left?
(d) What is the half-life of strontium-90?
2. The decay rate of a Tritium is 5.36% per year. What is its
half-life? solution
3. The half-life of radium is 1690 years. If 10
grams are present now, how much will be present in 50 years? solution
4. Solve the following:
(a) \(\displaystyle{ 8^{x + 3} = 16^{x - 1} }\) solution
(b) \(\displaystyle{ \frac{8}{27} = \left(\frac{3}{2}\right)^x }\) solution
(c) \(\displaystyle{ (\sqrt 2)^{2 - 3x} = \frac{1}{8} }\) solution
(d) \(\displaystyle{ 3^{x^2 - 5x - 12} = 9 }\) solution
(e) \(\displaystyle{ 5^{x^2 - 3x - 35} = \left( \frac{1}{5}
\right)^x }\) solution