Section 3.1: Exponential Functions
1. Given the Exponential function $f(x)=16^x$. Find the exact value the following. solution
(a) $f(0) $ (b) $f(-2)$ (c) $f(-1)$ (d) $f\left(\frac{1}{2}\right)$ (e) $f\left(-\frac{1}{4}\right)$
2. 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?
3. The decay rate of a Tritium is 5.36% per year. What is its
half-life? solution
4. The half-life of radium is 1690 years. If 10 grams are present now, how much will be present in 50 years? solution