The radioactive isotope Uranium-235, used for nuclear power, has a half-life of 704 million years. Assume an initial amount of 1.7 kg . Use the the formula \( A(t)=A_{0} e^{k t} \) to model the situation, where \( A_{0} \) is the initial amount of the material and \( k \) is a constant representing the rate of decay per million years. a) Find the exact value of \( k \), the decay constant. Round to 6 decimal places or enter an exact answer. \( k= \) b) Using the \( k \) value from part (a), find a function that gives the amount of the isotope \( A \) that remains after \( t \) million years. c) How long will it take for \( 40 \% \) of the material to decay? Round to the nearest tenth of a year. (HINT: If \( 40 \% \) of the material decays, how much is left?) Time:

Divide the polynomials. The form of your answer should either be \( p(x) \) or \( p(x)+\frac{k}{x-4} \) where \( p(x) \) is a polynomial and \( k \) is an integer. \( \frac{4 x^{3}-14 x^{2}-7 x-4}{x-4}=\square \)

El cantante favorito de Priya ha grabado 6 discos que tienen 75 canciones en total. Priya quiere hacer una lista de reproducción con 10 de esas canciones, y no repetirá 1 de las 75 canciones. Se puede usar la fórmula de permutación \( n \mathrm{Pr} \) para encontrar el número de maneras únicas en las que Priya puede elegir y ordenar las canciones de la lista de reproducción. ¿Cuáles son los valores apropiados de \( n \) y \( r \) ?

Simplify the expression and write the answer with positive exponents only. \( \left(6 y^{4} b^{-7}\right)\left(3 y^{-5} b^{8}\right) \)

If the partent function \( g(x)=\left(\frac{1}{7}\right)^{x} \) is compressed to \( \frac{1}{7} \) of its height, shifted vertically up 3 units, and shifted horizontally right by 7 units, what is the equation of the transformed function?

Multiply. Your answer should be a monomial in standard form. \( \left(-b^{7}\right)\left(7 b^{4}\right)=\square \)